289.2.a.a |
\(1\) |
\(2.308\) |
\(\Q\) |
None |
\(-1\) |
\(0\) |
\(2\) |
\(-4\) |
\(+\) |
\(q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots\)
|
289.2.a.b |
\(2\) |
\(2.308\) |
\(\Q(\sqrt{13}) \) |
None |
\(-1\) |
\(-1\) |
\(-1\) |
\(-3\) |
\(+\) |
\(q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots\)
|
289.2.a.c |
\(2\) |
\(2.308\) |
\(\Q(\sqrt{13}) \) |
None |
\(-1\) |
\(1\) |
\(1\) |
\(3\) |
\(-\) |
\(q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots\)
|
289.2.a.d |
\(3\) |
\(2.308\) |
\(\Q(\zeta_{18})^+\) |
None |
\(0\) |
\(-3\) |
\(-6\) |
\(0\) |
\(+\) |
\(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
|
289.2.a.e |
\(3\) |
\(2.308\) |
\(\Q(\zeta_{18})^+\) |
None |
\(0\) |
\(3\) |
\(6\) |
\(0\) |
\(-\) |
\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
|
289.2.a.f |
\(4\) |
\(2.308\) |
\(\Q(\zeta_{16})^+\) |
None |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
\(-\) |
\(q+(1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots\)
|
289.2.b.a |
\(2\) |
\(2.308\) |
\(\Q(\sqrt{-1}) \) |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+q^{2}-q^{4}+iq^{5}+2iq^{7}-3q^{8}+\cdots\)
|
289.2.b.b |
\(4\) |
\(2.308\) |
4.0.2048.2 |
None |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)
|
289.2.b.c |
\(4\) |
\(2.308\) |
\(\Q(i, \sqrt{13})\) |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
|
289.2.b.d |
\(6\) |
\(2.308\) |
6.0.419904.1 |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{2}-\beta _{4})q^{4}+\cdots\)
|
289.2.c.a |
\(4\) |
\(2.308\) |
\(\Q(\zeta_{8})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{8}^{2}q^{2}+q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{3}q^{7}+\cdots\)
|
289.2.c.b |
\(8\) |
\(2.308\) |
8.0.1871773696.1 |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
|
289.2.c.c |
\(8\) |
\(2.308\) |
\(\Q(\zeta_{16})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\zeta_{16}^{2}-\zeta_{16}^{3})q^{2}+(-\zeta_{16}+\zeta_{16}^{7})q^{3}+\cdots\)
|
289.2.c.d |
\(12\) |
\(2.308\) |
12.0.\(\cdots\).1 |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\beta _{4}-\beta _{9})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\)
|
289.2.d.a |
\(4\) |
\(2.308\) |
\(\Q(\zeta_{8})\) |
None |
\(-4\) |
\(4\) |
\(0\) |
\(4\) |
|
\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
|
289.2.d.b |
\(4\) |
\(2.308\) |
\(\Q(\zeta_{8})\) |
None |
\(4\) |
\(-4\) |
\(-4\) |
\(-4\) |
|
\(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
|
289.2.d.c |
\(4\) |
\(2.308\) |
\(\Q(\zeta_{8})\) |
None |
\(4\) |
\(4\) |
\(4\) |
\(4\) |
|
\(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
|
289.2.d.d |
\(8\) |
\(2.308\) |
\(\Q(\zeta_{16})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots\)
|
289.2.d.e |
\(16\) |
\(2.308\) |
16.0.\(\cdots\).1 |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\beta _{3}+\beta _{5})q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-2\beta _{8}+\cdots)q^{4}+\cdots\)
|
289.2.d.f |
\(24\) |
\(2.308\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
289.2.f.a |
\(384\) |
\(2.308\) |
|
None |
\(-13\) |
\(-13\) |
\(-43\) |
\(-13\) |
|
|
289.2.g.a |
\(384\) |
\(2.308\) |
|
None |
\(-17\) |
\(-17\) |
\(17\) |
\(-17\) |
|
|
289.2.h.a |
\(768\) |
\(2.308\) |
|
None |
\(-34\) |
\(-34\) |
\(-34\) |
\(-34\) |
|
|
289.2.i.a |
\(1600\) |
\(2.308\) |
|
None |
\(-64\) |
\(-64\) |
\(-68\) |
\(-64\) |
|
|
289.3.e.a |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(-8\) |
\(-16\) |
\(-8\) |
\(-16\) |
|
\(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-2-2\zeta_{16}+\cdots)q^{3}+\cdots\)
|
289.3.e.b |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(-8\) |
\(-8\) |
\(0\) |
\(-8\) |
|
\(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
|
289.3.e.c |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(-8\) |
\(8\) |
\(-16\) |
\(-8\) |
|
\(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
|
289.3.e.d |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(-8\) |
\(8\) |
\(0\) |
\(8\) |
|
\(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
|
289.3.e.e |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(-8\) |
\(16\) |
\(8\) |
\(16\) |
|
\(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(2+2\zeta_{16}+\cdots)q^{3}+\cdots\)
|
289.3.e.f |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(0\) |
\(-8\) |
\(-8\) |
\(8\) |
|
\(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots\)
|
289.3.e.g |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(0\) |
\(0\) |
\(24\) |
\(16\) |
|
\(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
|
289.3.e.h |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(0\) |
\(8\) |
\(8\) |
\(-8\) |
|
\(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
|
289.3.e.i |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(8\) |
\(-8\) |
\(-16\) |
\(8\) |
|
\(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
|
289.3.e.j |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(8\) |
\(-8\) |
\(16\) |
\(-8\) |
|
\(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots\)
|
289.3.e.k |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(8\) |
\(0\) |
\(-16\) |
\(40\) |
|
\(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
|
289.3.e.l |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(8\) |
\(0\) |
\(16\) |
\(-40\) |
|
\(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
|
289.3.e.m |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(8\) |
\(8\) |
\(16\) |
\(-8\) |
|
\(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
|
289.3.e.n |
\(8\) |
\(7.875\) |
\(\Q(\zeta_{16})\) |
None |
\(8\) |
\(8\) |
\(-16\) |
\(8\) |
|
\(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
|
289.3.e.o |
\(16\) |
\(7.875\) |
16.0.\(\cdots\).1 |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{6}q^{2}+\beta _{11}q^{3}+3\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots\)
|
289.3.e.p |
\(32\) |
\(7.875\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
289.3.e.q |
\(48\) |
\(7.875\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
289.3.e.r |
\(96\) |
\(7.875\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
289.3.j.a |
\(6400\) |
\(7.875\) |
|
None |
\(-128\) |
\(-128\) |
\(-128\) |
\(-128\) |
|
|
289.4.a.a |
\(1\) |
\(17.052\) |
\(\Q\) |
None |
\(-3\) |
\(8\) |
\(-6\) |
\(28\) |
\(+\) |
\(q-3q^{2}+8q^{3}+q^{4}-6q^{5}-24q^{6}+\cdots\)
|
289.4.a.b |
\(3\) |
\(17.052\) |
3.3.2636.1 |
None |
\(1\) |
\(-4\) |
\(8\) |
\(-22\) |
\(+\) |
\(q+(\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
|
289.4.a.c |
\(4\) |
\(17.052\) |
4.4.2555057.1 |
None |
\(1\) |
\(-2\) |
\(14\) |
\(36\) |
\(+\) |
\(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
|
289.4.a.d |
\(4\) |
\(17.052\) |
4.4.2555057.1 |
None |
\(1\) |
\(2\) |
\(-14\) |
\(-36\) |
\(-\) |
\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
|
289.4.a.e |
\(4\) |
\(17.052\) |
4.4.4669632.2 |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
\(+\) |
\(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+\cdots\)
|
289.4.a.f |
\(8\) |
\(17.052\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(8\) |
\(0\) |
\(0\) |
\(0\) |
\(+\) |
\(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(5-\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots\)
|
289.4.a.g |
\(12\) |
\(17.052\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
\(-8\) |
\(0\) |
\(0\) |
\(0\) |
\(-\) |
\(q+(-1+\beta _{5})q^{2}+\beta _{7}q^{3}+(2+2\beta _{1}+\cdots)q^{4}+\cdots\)
|