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 |
$2$ |
$1$ |
$1$ |
$0.019$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) |
\(\Q(\sqrt{13}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\) |
52.1.j.a |
$52$ |
$1$ |
52.j |
52.j |
$6$ |
$2$ |
$1$ |
$0.026$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\) |
55.1.d.a |
$55$ |
$1$ |
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 |
$2$ |
$1$ |
$1$ |
$0.028$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots\) |
57.1.h.a |
$57$ |
$1$ |
57.h |
57.h |
$6$ |
$2$ |
$1$ |
$0.028$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots\) |
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 |
$2$ |
$1$ |
$1$ |
$0.034$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots\) |
68.1.f.a |
$68$ |
$1$ |
68.f |
68.f |
$4$ |
$2$ |
$1$ |
$0.034$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\) |
72.1.p.a |
$72$ |
$1$ |
72.p |
72.p |
$6$ |
$2$ |
$1$ |
$0.036$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\) |
77.1.j.a |
$77$ |
$1$ |
77.j |
77.j |
$10$ |
$4$ |
$1$ |
$0.038$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-7}) \) |
None |
|
$4$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\) |
80.1.h.a |
$80$ |
$1$ |
80.h |
20.d |
$2$ |
$1$ |
$1$ |
$0.040$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots\) |
84.1.p.a |
$84$ |
$1$ |
84.p |
21.h |
$6$ |
$2$ |
$1$ |
$0.042$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\) |
88.1.l.a |
$88$ |
$1$ |
88.l |
88.l |
$10$ |
$4$ |
$1$ |
$0.044$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots\) |
93.1.l.a |
$93$ |
$1$ |
93.l |
93.l |
$10$ |
$4$ |
$1$ |
$0.046$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\) |
95.1.d.a |
$95$ |
$1$ |
95.d |
95.d |
$2$ |
$1$ |
$1$ |
$0.047$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots\) |
95.1.d.b |
$95$ |
$1$ |
95.d |
95.d |
$2$ |
$2$ |
$2$ |
$0.047$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-95}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\) |
99.1.h.a |
$99$ |
$1$ |
99.h |
99.h |
$6$ |
$2$ |
$1$ |
$0.049$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-11}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(1\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\) |
100.1.j.a |
$100$ |
$1$ |
100.j |
100.j |
$10$ |
$4$ |
$1$ |
$0.050$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots\) |
111.1.d.a |
$111$ |
$1$ |
111.d |
111.d |
$2$ |
$1$ |
$1$ |
$0.055$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) |
\(\Q(\sqrt{37}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots\) |
111.1.d.b |
$111$ |
$1$ |
111.d |
111.d |
$2$ |
$2$ |
$2$ |
$0.055$ |
\(\Q(\sqrt{2}) \) |
$D_{4}$ |
\(\Q(\sqrt{-111}) \) |
None |
✓ |
$4$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots\) |
111.1.h.a |
$111$ |
$1$ |
111.h |
111.h |
$6$ |
$2$ |
$1$ |
$0.055$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
111.1.i.a |
$111$ |
$1$ |
111.i |
111.i |
$6$ |
$2$ |
$1$ |
$0.055$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
112.1.l.a |
$112$ |
$1$ |
112.l |
112.l |
$4$ |
$2$ |
$1$ |
$0.056$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
\(\Q(\sqrt{-7}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots\) |
116.1.j.a |
$116$ |
$1$ |
116.j |
116.j |
$14$ |
$6$ |
$1$ |
$0.058$ |
\(\Q(\zeta_{14})\) |
$D_{7}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots\) |
117.1.j.a |
$117$ |
$1$ |
117.j |
13.d |
$4$ |
$2$ |
$1$ |
$0.058$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots\) |
124.1.i.a |
$124$ |
$1$ |
124.i |
124.i |
$6$ |
$4$ |
$2$ |
$0.062$ |
\(\Q(\zeta_{12})\) |
$A_{4}$ |
None |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots\) |
128.1.d.a |
$128$ |
$1$ |
128.d |
8.d |
$2$ |
$1$ |
$1$ |
$0.064$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
\(\Q(\sqrt{2}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots\) |
129.1.l.a |
$129$ |
$1$ |
129.l |
129.l |
$14$ |
$6$ |
$1$ |
$0.064$ |
\(\Q(\zeta_{14})\) |
$D_{7}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\) |
133.1.m.a |
$133$ |
$1$ |
133.m |
133.m |
$6$ |
$4$ |
$2$ |
$0.066$ |
\(\Q(\zeta_{12})\) |
$A_{4}$ |
None |
None |
|
$4$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots\) |
133.1.r.a |
$133$ |
$1$ |
133.r |
133.r |
$6$ |
$2$ |
$1$ |
$0.066$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-19}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
136.1.e.a |
$136$ |
$1$ |
136.e |
136.e |
$2$ |
$1$ |
$1$ |
$0.068$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) |
\(\Q(\sqrt{17}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots\) |
136.1.j.a |
$136$ |
$1$ |
136.j |
136.j |
$4$ |
$2$ |
$1$ |
$0.068$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}+(-1-i)q^{3}-q^{4}+(-1+i+\cdots)q^{6}+\cdots\) |
136.1.p.a |
$136$ |
$1$ |
136.p |
136.p |
$8$ |
$4$ |
$1$ |
$0.068$ |
\(\Q(\zeta_{8})\) |
$D_{8}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\) |
140.1.p.a |
$140$ |
$1$ |
140.p |
140.p |
$6$ |
$2$ |
$1$ |
$0.070$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-5}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(-1\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\) |
140.1.p.b |
$140$ |
$1$ |
140.p |
140.p |
$6$ |
$2$ |
$1$ |
$0.070$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-5}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(-1\) |
\(1\) |
$1$ |
|
\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\) |
144.1.g.a |
$144$ |
$1$ |
144.g |
4.b |
$2$ |
$1$ |
$1$ |
$0.072$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots\) |
145.1.f.a |
$145$ |
$1$ |
145.f |
145.f |
$4$ |
$2$ |
$1$ |
$0.072$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{5}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+iq^{4}-iq^{5}+iq^{9}+(-1-i)q^{11}+\cdots\) |
145.1.h.a |
$145$ |
$1$ |
145.h |
145.h |
$4$ |
$2$ |
$1$ |
$0.072$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
None |
\(\Q(\sqrt{29}) \) |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-iq^{4}-iq^{5}+(-1+i)q^{7}+iq^{9}+\cdots\) |
147.1.l.a |
$147$ |
$1$ |
147.l |
147.l |
$14$ |
$6$ |
$1$ |
$0.073$ |
\(\Q(\zeta_{14})\) |
$D_{7}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots\) |
148.1.i.a |
$148$ |
$1$ |
148.i |
148.i |
$6$ |
$2$ |
$1$ |
$0.074$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\) |
148.1.p.a |
$148$ |
$1$ |
148.p |
148.p |
$18$ |
$6$ |
$1$ |
$0.074$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-3\) |
\(0\) |
$1$ |
|
\(q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots\) |
152.1.k.a |
$152$ |
$1$ |
152.k |
152.k |
$6$ |
$2$ |
$1$ |
$0.076$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\) |
152.1.u.a |
$152$ |
$1$ |
152.u |
152.u |
$18$ |
$6$ |
$1$ |
$0.076$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-2}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-3\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots\) |
155.1.c.a |
$155$ |
$1$ |
155.c |
155.c |
$2$ |
$1$ |
$1$ |
$0.077$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-155}) \) |
\(\Q(\sqrt{5}) \) |
✓ |
$4$ |
$0$ |
\(0\) |
\(0\) |
\(-1\) |
\(0\) |
$1$ |
|
\(q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots\) |
155.1.c.b |
$155$ |
$1$ |
155.c |
155.c |
$2$ |
$2$ |
$2$ |
$0.077$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
\(\Q(\sqrt{-31}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(1\) |
\(0\) |
$1$ |
|
\(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\) |
156.1.o.a |
$156$ |
$1$ |
156.o |
39.i |
$6$ |
$2$ |
$1$ |
$0.078$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots\) |
156.1.s.a |
$156$ |
$1$ |
156.s |
39.h |
$6$ |
$2$ |
$1$ |
$0.078$ |
\(\Q(\sqrt{-3}) \) |
$D_{6}$ |
\(\Q(\sqrt{-3}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(-3\) |
$1$ |
|
\(q+\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
160.1.p.a |
$160$ |
$1$ |
160.p |
5.c |
$4$ |
$2$ |
$1$ |
$0.080$ |
\(\Q(\sqrt{-1}) \) |
$D_{4}$ |
\(\Q(\sqrt{-1}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots\) |
161.1.l.a |
$161$ |
$1$ |
161.l |
161.l |
$22$ |
$10$ |
$1$ |
$0.080$ |
\(\Q(\zeta_{22})\) |
$D_{11}$ |
\(\Q(\sqrt{-7}) \) |
None |
|
$4$ |
$0$ |
\(-2\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+(-\zeta_{22}+\zeta_{22}^{8})q^{2}+(\zeta_{22}^{2}-\zeta_{22}^{5}+\cdots)q^{4}+\cdots\) |
164.1.d.a |
$164$ |
$1$ |
164.d |
164.d |
$2$ |
$1$ |
$1$ |
$0.082$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) |
\(\Q(\sqrt{41}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(0\) |
\(-2\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots\) |