1680.1.bb.a |
\(1\) |
\(0.838\) |
\(\Q\) |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-105}) \) |
\(\Q(\sqrt{21}) \) |
\(0\) |
\(-1\) |
\(-1\) |
\(-1\) |
|
\(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{15}+q^{21}+\cdots\)
|
1680.1.bb.b |
\(1\) |
\(0.838\) |
\(\Q\) |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-105}) \) |
\(\Q(\sqrt{21}) \) |
\(0\) |
\(-1\) |
\(1\) |
\(1\) |
|
\(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{15}-q^{21}+\cdots\)
|
1680.1.bb.c |
\(1\) |
\(0.838\) |
\(\Q\) |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-105}) \) |
\(\Q(\sqrt{21}) \) |
\(0\) |
\(1\) |
\(-1\) |
\(1\) |
|
\(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{15}+q^{21}+\cdots\)
|
1680.1.bb.d |
\(1\) |
\(0.838\) |
\(\Q\) |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-105}) \) |
\(\Q(\sqrt{21}) \) |
\(0\) |
\(1\) |
\(1\) |
\(-1\) |
|
\(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{15}-q^{21}+\cdots\)
|
1680.1.bb.e |
\(2\) |
\(0.838\) |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{15}) \) |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+iq^{3}-iq^{5}-iq^{7}-q^{9}-q^{11}+\cdots\)
|
1680.1.bb.f |
\(2\) |
\(0.838\) |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-21}) \) |
\(\Q(\sqrt{15}) \) |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-iq^{3}-iq^{5}+iq^{7}-q^{9}+q^{11}+\cdots\)
|
1680.1.bb.g |
\(4\) |
\(0.838\) |
\(\Q(\zeta_{12})\) |
\(\Q(\sqrt{-35}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
|
1680.1.bb.h |
\(4\) |
\(0.838\) |
\(\Q(\zeta_{12})\) |
\(\Q(\sqrt{-35}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
|
1680.1.dp.a |
\(2\) |
\(0.838\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-5}) \) |
None |
\(0\) |
\(-2\) |
\(-1\) |
\(-1\) |
|
\(q-q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+q^{9}+\zeta_{6}q^{15}+\cdots\)
|
1680.1.dp.b |
\(2\) |
\(0.838\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-5}) \) |
None |
\(0\) |
\(-1\) |
\(1\) |
\(-1\) |
|
\(q-\zeta_{6}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
|
1680.1.dp.c |
\(2\) |
\(0.838\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-5}) \) |
None |
\(0\) |
\(1\) |
\(1\) |
\(1\) |
|
\(q+\zeta_{6}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
|
1680.1.dp.d |
\(2\) |
\(0.838\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-5}) \) |
None |
\(0\) |
\(2\) |
\(-1\) |
\(1\) |
|
\(q+q^{3}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{9}-\zeta_{6}q^{15}+\cdots\)
|
1680.2.a.a |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(-1\) |
\(-\) |
\(q-q^{3}-q^{5}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
|
1680.2.a.b |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(-1\) |
\(-\) |
\(q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
|
1680.2.a.c |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(-1\) |
\(+\) |
\(q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
|
1680.2.a.d |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(1\) |
\(-\) |
\(q-q^{3}-q^{5}+q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
|
1680.2.a.e |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(1\) |
\(-\) |
\(q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
|
1680.2.a.f |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(1\) |
\(-1\) |
\(+\) |
\(q-q^{3}+q^{5}-q^{7}+q^{9}-6q^{13}-q^{15}+\cdots\)
|
1680.2.a.g |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(1\) |
\(-1\) |
\(+\) |
\(q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
|
1680.2.a.h |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(1\) |
\(1\) |
\(+\) |
\(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
|
1680.2.a.i |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(1\) |
\(1\) |
\(-\) |
\(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
|
1680.2.a.j |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(1\) |
\(1\) |
\(-\) |
\(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
|
1680.2.a.k |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(-1\) |
\(-1\) |
\(-\) |
\(q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
|
1680.2.a.l |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(-1\) |
\(-1\) |
\(-\) |
\(q+q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
|
1680.2.a.m |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(-1\) |
\(1\) |
\(+\) |
\(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
|
1680.2.a.n |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(-1\) |
\(1\) |
\(-\) |
\(q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
|
1680.2.a.o |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(-1\) |
\(1\) |
\(-\) |
\(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
|
1680.2.a.p |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(1\) |
\(-1\) |
\(+\) |
\(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
|
1680.2.a.q |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(1\) |
\(-1\) |
\(-\) |
\(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
|
1680.2.a.r |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(1\) |
\(-1\) |
\(-\) |
\(q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
|
1680.2.a.s |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(1\) |
\(1\) |
\(-\) |
\(q+q^{3}+q^{5}+q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
|
1680.2.a.t |
\(1\) |
\(13.415\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(1\) |
\(1\) |
\(-\) |
\(q+q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
|
1680.2.a.u |
\(2\) |
\(13.415\) |
\(\Q(\sqrt{2}) \) |
None |
None |
\(0\) |
\(-2\) |
\(2\) |
\(-2\) |
\(-\) |
\(q-q^{3}+q^{5}-q^{7}+q^{9}+\beta q^{11}+2q^{13}+\cdots\)
|
1680.2.a.v |
\(2\) |
\(13.415\) |
\(\Q(\sqrt{5}) \) |
None |
None |
\(0\) |
\(2\) |
\(-2\) |
\(-2\) |
\(+\) |
\(q+q^{3}-q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
|
1680.2.d.a |
\(4\) |
\(13.415\) |
\(\Q(i, \sqrt{6})\) |
None |
None |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
|
\(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
|
1680.2.d.b |
\(4\) |
\(13.415\) |
\(\Q(i, \sqrt{6})\) |
None |
None |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
|
\(q+q^{3}-\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
|
1680.2.d.c |
\(12\) |
\(13.415\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
None |
\(0\) |
\(-12\) |
\(0\) |
\(4\) |
|
\(q-q^{3}-\beta _{1}q^{5}-\beta _{9}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots\)
|
1680.2.d.d |
\(12\) |
\(13.415\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
None |
\(0\) |
\(12\) |
\(0\) |
\(-4\) |
|
\(q+q^{3}+\beta _{1}q^{5}+\beta _{8}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots\)
|
1680.2.f.a |
\(2\) |
\(13.415\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-3\) |
\(2\) |
\(-4\) |
|
\(q+(-2+\zeta_{6})q^{3}+q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
|
1680.2.f.b |
\(2\) |
\(13.415\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(-4\) |
|
\(q+\zeta_{6}q^{3}-q^{5}+(-2-\zeta_{6})q^{7}-3q^{9}+\cdots\)
|
1680.2.f.c |
\(2\) |
\(13.415\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(-4\) |
|
\(q-\zeta_{6}q^{3}+q^{5}+(-2+\zeta_{6})q^{7}-3q^{9}+\cdots\)
|
1680.2.f.d |
\(2\) |
\(13.415\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(3\) |
\(-2\) |
\(-4\) |
|
\(q+(2-\zeta_{6})q^{3}-q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
|
1680.2.f.e |
\(4\) |
\(13.415\) |
\(\Q(i, \sqrt{5})\) |
None |
None |
\(0\) |
\(-2\) |
\(-4\) |
\(-6\) |
|
\(q+(\beta _{1}+\beta _{2})q^{3}-q^{5}+(-1+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
|
1680.2.f.f |
\(4\) |
\(13.415\) |
\(\Q(i, \sqrt{5})\) |
None |
None |
\(0\) |
\(-2\) |
\(-4\) |
\(6\) |
|
\(q+(-1-\beta _{1})q^{3}-q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
|
1680.2.f.g |
\(4\) |
\(13.415\) |
\(\Q(\sqrt{-3}, \sqrt{-11})\) |
None |
None |
\(0\) |
\(-1\) |
\(4\) |
\(8\) |
|
\(q-\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
|
1680.2.f.h |
\(4\) |
\(13.415\) |
\(\Q(\sqrt{-3}, \sqrt{-11})\) |
None |
None |
\(0\) |
\(1\) |
\(-4\) |
\(8\) |
|
\(q+\beta _{1}q^{3}-q^{5}+(2-\beta _{2})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
|
1680.2.f.i |
\(4\) |
\(13.415\) |
\(\Q(i, \sqrt{5})\) |
None |
None |
\(0\) |
\(2\) |
\(4\) |
\(-6\) |
|
\(q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+(-1-2\beta _{2}+\cdots)q^{7}+\cdots\)
|
1680.2.f.j |
\(4\) |
\(13.415\) |
\(\Q(i, \sqrt{5})\) |
None |
None |
\(0\) |
\(2\) |
\(4\) |
\(6\) |
|
\(q+(1+\beta _{1})q^{3}+q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots\)
|
1680.2.f.k |
\(16\) |
\(13.415\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(-16\) |
\(-2\) |
|
\(q+\beta _{3}q^{3}-q^{5}-\beta _{9}q^{7}+\beta _{7}q^{9}+\beta _{8}q^{11}+\cdots\)
|
1680.2.f.l |
\(16\) |
\(13.415\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(16\) |
\(-2\) |
|
\(q-\beta _{3}q^{3}+q^{5}-\beta _{4}q^{7}+\beta _{7}q^{9}+\beta _{8}q^{11}+\cdots\)
|