300.1.b.a |
\(2\) |
\(0.150\) |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-iq^{3}-iq^{7}-q^{9}+iq^{13}+q^{19}+\cdots\)
|
300.1.g.a |
\(1\) |
\(0.150\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(-1\) |
\(0\) |
\(1\) |
|
\(q-q^{3}+q^{7}+q^{9}+q^{13}-q^{19}-q^{21}+\cdots\)
|
300.1.g.b |
\(1\) |
\(0.150\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(1\) |
\(0\) |
\(-1\) |
|
\(q+q^{3}-q^{7}+q^{9}-q^{13}-q^{19}-q^{21}+\cdots\)
|
300.1.l.a |
\(4\) |
\(0.150\) |
\(\Q(\zeta_{8})\) |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-5}) \) |
\(\Q(\sqrt{3}) \) |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots\)
|
300.2.a.a |
\(1\) |
\(2.396\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(0\) |
\(-4\) |
\(+\) |
\(q-q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots\)
|
300.2.a.b |
\(1\) |
\(2.396\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(0\) |
\(1\) |
\(-\) |
\(q-q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots\)
|
300.2.a.c |
\(1\) |
\(2.396\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(0\) |
\(-1\) |
\(-\) |
\(q+q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots\)
|
300.2.a.d |
\(1\) |
\(2.396\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(0\) |
\(4\) |
\(-\) |
\(q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots\)
|
300.2.d.a |
\(2\) |
\(2.396\) |
\(\Q(\sqrt{-1}) \) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots\)
|
300.2.e.a |
\(4\) |
\(2.396\) |
\(\Q(\sqrt{3}, \sqrt{-5})\) |
\(\Q(\sqrt{-15}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots\)
|
300.2.e.b |
\(4\) |
\(2.396\) |
\(\Q(\sqrt{2}, \sqrt{-5})\) |
\(\Q(\sqrt{-5}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots\)
|
300.2.e.c |
\(8\) |
\(2.396\) |
8.0.342102016.5 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{5}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
|
300.2.e.d |
\(8\) |
\(2.396\) |
8.0.4521217600.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
|
300.2.e.e |
\(8\) |
\(2.396\) |
8.0.4521217600.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
|
300.2.h.a |
\(8\) |
\(2.396\) |
8.0.342102016.5 |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
|
300.2.h.b |
\(8\) |
\(2.396\) |
8.0.342102016.5 |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
|
300.2.h.c |
\(16\) |
\(2.396\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}-\beta _{10}q^{3}-\beta _{4}q^{4}-\beta _{12}q^{6}+\cdots\)
|
300.2.i.a |
\(4\) |
\(2.396\) |
\(\Q(i, \sqrt{5})\) |
None |
None |
\(0\) |
\(-2\) |
\(0\) |
\(4\) |
|
\(q+(-1+\beta _{3})q^{3}+(1-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
|
300.2.i.b |
\(4\) |
\(2.396\) |
\(\Q(i, \sqrt{6})\) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{3}+2\beta _{3}q^{7}+3\beta _{2}q^{9}+4\beta _{1}q^{13}+\cdots\)
|
300.2.i.c |
\(4\) |
\(2.396\) |
\(\Q(i, \sqrt{6})\) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{3}-3\beta _{3}q^{7}+3\beta _{2}q^{9}-\beta _{1}q^{13}+\cdots\)
|
300.2.j.a |
\(8\) |
\(2.396\) |
\(\Q(\zeta_{24})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{5})q^{2}+\zeta_{24}q^{3}+\cdots\)
|
300.2.j.b |
\(8\) |
\(2.396\) |
8.0.157351936.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\beta _{2}+\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{4}+\cdots\)
|
300.2.j.c |
\(8\) |
\(2.396\) |
\(\Q(\zeta_{24})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}-\zeta_{24}^{5}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
|
300.2.j.d |
\(12\) |
\(2.396\) |
12.0.\(\cdots\).1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{8}+\beta _{9})q^{4}+\cdots\)
|
300.2.m.a |
\(8\) |
\(2.396\) |
\(\Q(\zeta_{15})\) |
None |
None |
\(0\) |
\(-2\) |
\(5\) |
\(-8\) |
|
\(q+\zeta_{15}^{5}q^{3}+(-1-2\zeta_{15}^{2}-\zeta_{15}^{3}+\cdots)q^{5}+\cdots\)
|
300.2.m.b |
\(8\) |
\(2.396\) |
8.0.26265625.1 |
None |
None |
\(0\) |
\(2\) |
\(-5\) |
\(8\) |
|
\(q+\beta _{3}q^{3}+(-1+\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
|
300.2.n.a |
\(224\) |
\(2.396\) |
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
300.2.o.a |
\(24\) |
\(2.396\) |
|
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
|
300.2.r.a |
\(224\) |
\(2.396\) |
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
300.2.w.a |
\(240\) |
\(2.396\) |
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
300.2.x.a |
\(80\) |
\(2.396\) |
|
None |
None |
\(0\) |
\(-2\) |
\(0\) |
\(4\) |
|
|
300.3.b.a |
\(2\) |
\(8.174\) |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+3iq^{3}+2iq^{7}-9q^{9}+22iq^{13}+\cdots\)
|
300.3.b.b |
\(2\) |
\(8.174\) |
\(\Q(\sqrt{-1}) \) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+3iq^{3}-13iq^{7}-9q^{9}-23iq^{13}+\cdots\)
|
300.3.b.c |
\(4\) |
\(8.174\) |
\(\Q(i, \sqrt{5})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{1}q^{7}+(1-2\beta _{2}+\cdots)q^{9}+\cdots\)
|
300.3.b.d |
\(4\) |
\(8.174\) |
\(\Q(i, \sqrt{35})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{3}-8\beta _{2}q^{7}+(9+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots\)
|
300.3.c.a |
\(2\) |
\(8.174\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
|
300.3.c.b |
\(2\) |
\(8.174\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
|
300.3.c.c |
\(2\) |
\(8.174\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
|
300.3.c.d |
\(8\) |
\(8.174\) |
8.0.85100625.1 |
None |
None |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{5}q^{2}+\beta _{6}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
|
300.3.c.e |
\(8\) |
\(8.174\) |
8.0.4069419264.1 |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{4}q^{2}-\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
|
300.3.c.f |
\(8\) |
\(8.174\) |
8.0.6080256576.2 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{5}q^{2}-\beta _{2}q^{3}+(1-\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
|
300.3.c.g |
\(8\) |
\(8.174\) |
8.0.4069419264.1 |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
|
300.3.f.a |
\(4\) |
\(8.174\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
|
300.3.f.b |
\(16\) |
\(8.174\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{12}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
|
300.3.f.c |
\(16\) |
\(8.174\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\)
|
300.3.g.a |
\(1\) |
\(8.174\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(-3\) |
\(0\) |
\(-13\) |
|
\(q-3q^{3}-13q^{7}+9q^{9}+23q^{13}+11q^{19}+\cdots\)
|
300.3.g.b |
\(1\) |
\(8.174\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(3\) |
\(0\) |
\(-2\) |
|
\(q+3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots\)
|
300.3.g.c |
\(1\) |
\(8.174\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(3\) |
\(0\) |
\(13\) |
|
\(q+3q^{3}+13q^{7}+9q^{9}-23q^{13}+11q^{19}+\cdots\)
|
300.3.g.d |
\(2\) |
\(8.174\) |
\(\Q(\sqrt{-5}) \) |
None |
None |
\(0\) |
\(-4\) |
\(0\) |
\(-4\) |
|
\(q+(-2+\beta )q^{3}-2q^{7}+(-1-4\beta )q^{9}+\cdots\)
|
300.3.g.e |
\(2\) |
\(8.174\) |
\(\Q(\sqrt{-5}) \) |
None |
None |
\(0\) |
\(-4\) |
\(0\) |
\(16\) |
|
\(q+(-2+\beta )q^{3}+8q^{7}+(-1-4\beta )q^{9}+\cdots\)
|