Label |
Level |
Weight |
Char |
Prim |
Char order |
Dim |
Rel. Dim |
$A$ |
Field |
Image |
CM |
RM |
Self-dual |
Inner twists |
Rank* |
Traces |
Coefficient ring index |
Sato-Tate |
$q$-expansion |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
39.1.d.a |
$39$ |
$1$ |
39.d |
39.d |
$2$ |
$1$ |
$1$ |
$0.019$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) |
\(\Q(\sqrt{13}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\) |
55.1.d.a |
$55$ |
$1$ |
55.d |
55.d |
$2$ |
$1$ |
$1$ |
$0.027$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots\) |
56.1.h.a |
$56$ |
$1$ |
56.h |
56.h |
$2$ |
$1$ |
$1$ |
$0.028$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots\) |
63.1.d.a |
$63$ |
$1$ |
63.d |
7.b |
$2$ |
$1$ |
$1$ |
$0.031$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) |
\(\Q(\sqrt{21}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots\) |
68.1.d.a |
$68$ |
$1$ |
68.d |
68.d |
$2$ |
$1$ |
$1$ |
$0.034$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots\) |
80.1.h.a |
$80$ |
$1$ |
80.h |
20.d |
$2$ |
$1$ |
$1$ |
$0.040$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots\) |
95.1.d.a |
$95$ |
$1$ |
95.d |
95.d |
$2$ |
$1$ |
$1$ |
$0.047$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots\) |
111.1.d.a |
$111$ |
$1$ |
111.d |
111.d |
$2$ |
$1$ |
$1$ |
$0.055$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) |
\(\Q(\sqrt{37}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\) |
120.1.i.a |
$120$ |
$1$ |
120.i |
120.i |
$2$ |
$2$ |
$2$ |
$0.060$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) |
\(\Q(\sqrt{10}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots\) |
128.1.d.a |
$128$ |
$1$ |
128.d |
8.d |
$2$ |
$1$ |
$1$ |
$0.064$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots\) |
136.1.e.a |
$136$ |
$1$ |
136.e |
136.e |
$2$ |
$1$ |
$1$ |
$0.068$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots\) |
144.1.g.a |
$144$ |
$1$ |
144.g |
4.b |
$2$ |
$1$ |
$1$ |
$0.072$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots\) |
155.1.c.a |
$155$ |
$1$ |
155.c |
155.c |
$2$ |
$1$ |
$1$ |
$0.077$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\) |
164.1.d.a |
$164$ |
$1$ |
164.d |
164.d |
$2$ |
$1$ |
$1$ |
$0.082$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) |
\(\Q(\sqrt{41}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots\) |
171.1.c.a |
$171$ |
$1$ |
171.c |
19.b |
$2$ |
$1$ |
$1$ |
$0.085$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
\(\Q(\sqrt{57}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\cdots\) |
180.1.f.a |
$180$ |
$1$ |
180.f |
20.d |
$2$ |
$2$ |
$2$ |
$0.090$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) |
\(\Q(\sqrt{15}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots\) |
183.1.d.a |
$183$ |
$1$ |
183.d |
183.d |
$2$ |
$1$ |
$1$ |
$0.091$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-183}) \) |
\(\Q(\sqrt{61}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{3}-q^{4}+q^{9}-q^{12}-2q^{13}+q^{16}+\cdots\) |
184.1.e.a |
$184$ |
$1$ |
184.e |
184.e |
$2$ |
$1$ |
$1$ |
$0.092$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-46}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\) |
192.1.h.a |
$192$ |
$1$ |
192.h |
24.h |
$2$ |
$2$ |
$2$ |
$0.096$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) |
\(\Q(\sqrt{6}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{3}-q^{9}+iq^{19}-q^{25}+iq^{27}+\cdots\) |
196.1.c.a |
$196$ |
$1$ |
196.c |
4.b |
$2$ |
$1$ |
$1$ |
$0.098$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
\(\Q(\sqrt{7}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\) |
196.1.g.a |
$196$ |
$1$ |
196.g |
28.g |
$6$ |
$2$ |
$1$ |
$0.098$ |
\(\Q(\sqrt{-3}) \) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
\(\Q(\sqrt{7}) \) |
|
$8$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots\) |
203.1.c.a |
$203$ |
$1$ |
203.c |
203.c |
$2$ |
$1$ |
$1$ |
$0.101$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-203}) \) |
\(\Q(\sqrt{29}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{4}-q^{7}-q^{9}+q^{16}-2q^{23}+q^{25}+\cdots\) |
208.1.c.a |
$208$ |
$1$ |
208.c |
52.b |
$2$ |
$1$ |
$1$ |
$0.104$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-13}) \) |
\(\Q(\sqrt{13}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{9}-q^{13}-2q^{17}+q^{25}-2q^{29}+\cdots\) |
219.1.c.a |
$219$ |
$1$ |
219.c |
219.c |
$2$ |
$1$ |
$1$ |
$0.109$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-219}) \) |
\(\Q(\sqrt{73}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}-2q^{19}+\cdots\) |
224.1.h.a |
$224$ |
$1$ |
224.h |
56.h |
$2$ |
$1$ |
$1$ |
$0.112$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+q^{7}-q^{9}-2q^{23}-q^{25}+q^{49}+\cdots\) |
225.1.g.a |
$225$ |
$1$ |
225.g |
5.c |
$4$ |
$2$ |
$1$ |
$0.112$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) |
\(\Q(\sqrt{5}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots\) |
248.1.g.a |
$248$ |
$1$ |
248.g |
248.g |
$2$ |
$1$ |
$1$ |
$0.124$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-62}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+q^{2}+q^{4}-2q^{7}+q^{8}-q^{9}-2q^{14}+\cdots\) |
255.1.h.e |
$255$ |
$1$ |
255.h |
255.h |
$2$ |
$2$ |
$2$ |
$0.127$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-51}) \) |
\(\Q(\sqrt{85}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{3}-q^{4}-iq^{5}-q^{9}+iq^{12}+\cdots\) |
256.1.c.a |
$256$ |
$1$ |
256.c |
4.b |
$2$ |
$1$ |
$1$ |
$0.128$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{9}-2q^{17}-q^{25}-2q^{41}+q^{49}+\cdots\) |
259.1.b.a |
$259$ |
$1$ |
259.b |
259.b |
$2$ |
$1$ |
$1$ |
$0.129$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-259}) \) |
\(\Q(\sqrt{37}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{4}-q^{7}+q^{9}-2q^{11}+q^{16}-q^{25}+\cdots\) |
260.1.g.a |
$260$ |
$1$ |
260.g |
260.g |
$2$ |
$1$ |
$1$ |
$0.130$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{9}-q^{10}+\cdots\) |
260.1.g.b |
$260$ |
$1$ |
260.g |
260.g |
$2$ |
$1$ |
$1$ |
$0.130$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) |
\(\Q(\sqrt{65}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{9}-q^{10}+\cdots\) |
264.1.p.a |
$264$ |
$1$ |
264.p |
264.p |
$2$ |
$1$ |
$1$ |
$0.132$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-66}) \) |
\(\Q(\sqrt{33}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\) |
264.1.p.b |
$264$ |
$1$ |
264.p |
264.p |
$2$ |
$1$ |
$1$ |
$0.132$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-66}) \) |
\(\Q(\sqrt{33}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\) |
275.1.c.a |
$275$ |
$1$ |
275.c |
11.b |
$2$ |
$1$ |
$1$ |
$0.137$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{4}-q^{9}-q^{11}+q^{16}-2q^{31}+\cdots\) |
276.1.h.a |
$276$ |
$1$ |
276.h |
276.h |
$2$ |
$1$ |
$1$ |
$0.138$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-69}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\) |
276.1.h.b |
$276$ |
$1$ |
276.h |
276.h |
$2$ |
$1$ |
$1$ |
$0.138$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-69}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\) |
279.1.d.a |
$279$ |
$1$ |
279.d |
31.b |
$2$ |
$1$ |
$1$ |
$0.139$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-31}) \) |
\(\Q(\sqrt{93}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(2\) |
$1$ |
|
\(q-q^{4}+2q^{7}+q^{16}-2q^{19}-q^{25}+\cdots\) |
291.1.c.a |
$291$ |
$1$ |
291.c |
291.c |
$2$ |
$1$ |
$1$ |
$0.145$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-291}) \) |
\(\Q(\sqrt{97}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}-q^{25}+\cdots\) |
292.1.b.a |
$292$ |
$1$ |
292.b |
292.b |
$2$ |
$1$ |
$1$ |
$0.146$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-73}) \) |
\(\Q(\sqrt{73}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\) |
295.1.d.a |
$295$ |
$1$ |
295.d |
295.d |
$2$ |
$1$ |
$1$ |
$0.147$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-295}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q-q^{4}+q^{5}+q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\) |
299.1.c.a |
$299$ |
$1$ |
299.c |
299.c |
$2$ |
$1$ |
$1$ |
$0.149$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-299}) \) |
\(\Q(\sqrt{13}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-2q^{3}+q^{4}+3q^{9}-2q^{12}+q^{13}+\cdots\) |
300.1.l.a |
$300$ |
$1$ |
300.l |
60.l |
$4$ |
$4$ |
$2$ |
$0.150$ |
\(\Q(\zeta_{8})\) |
$D_{2}$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{3}) \) |
|
$16$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots\) |
308.1.g.a |
$308$ |
$1$ |
308.g |
308.g |
$2$ |
$1$ |
$1$ |
$0.154$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{9}+q^{11}+\cdots\) |
308.1.g.b |
$308$ |
$1$ |
308.g |
308.g |
$2$ |
$1$ |
$1$ |
$0.154$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) |
\(\Q(\sqrt{11}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}-q^{11}+\cdots\) |
320.1.h.a |
$320$ |
$1$ |
320.h |
20.d |
$2$ |
$1$ |
$1$ |
$0.160$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q+q^{5}-q^{9}+q^{25}-2q^{29}-2q^{41}+\cdots\) |
323.1.c.a |
$323$ |
$1$ |
323.c |
323.c |
$2$ |
$1$ |
$1$ |
$0.161$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-323}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{4}-q^{9}+q^{16}-q^{17}-q^{19}+q^{25}+\cdots\) |
327.1.d.b |
$327$ |
$1$ |
327.d |
327.d |
$2$ |
$1$ |
$1$ |
$0.163$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-327}) \) |
\(\Q(\sqrt{109}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(2\) |
$1$ |
|
\(q-q^{3}-q^{4}+2q^{7}+q^{9}+q^{12}+q^{16}+\cdots\) |
328.1.c.a |
$328$ |
$1$ |
328.c |
328.c |
$2$ |
$1$ |
$1$ |
$0.164$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-82}) \) |
\(\Q(\sqrt{41}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\) |
336.1.o.a |
$336$ |
$1$ |
336.o |
84.h |
$2$ |
$1$ |
$1$ |
$0.168$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{7}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-q^{3}+q^{7}+q^{9}+2q^{19}-q^{21}-q^{25}+\cdots\) |