672.1.ba.a |
\(2\) |
\(0.335\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-6}) \) |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(1\) |
|
\(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
|
672.1.ba.b |
\(2\) |
\(0.335\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-6}) \) |
None |
\(0\) |
\(1\) |
\(1\) |
\(1\) |
|
\(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
|
672.2.a.a |
\(1\) |
\(5.366\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(-4\) |
\(-1\) |
\(-\) |
\(q-q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
|
672.2.a.b |
\(1\) |
\(5.366\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(-2\) |
\(1\) |
\(+\) |
\(q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
|
672.2.a.c |
\(1\) |
\(5.366\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(0\) |
\(-1\) |
\(+\) |
\(q-q^{3}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
|
672.2.a.d |
\(1\) |
\(5.366\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(2\) |
\(-1\) |
\(-\) |
\(q-q^{3}+2q^{5}-q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
|
672.2.a.e |
\(1\) |
\(5.366\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(-4\) |
\(1\) |
\(+\) |
\(q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
|
672.2.a.f |
\(1\) |
\(5.366\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(-2\) |
\(-1\) |
\(+\) |
\(q+q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
|
672.2.a.g |
\(1\) |
\(5.366\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(0\) |
\(1\) |
\(-\) |
\(q+q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
|
672.2.a.h |
\(1\) |
\(5.366\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(2\) |
\(1\) |
\(-\) |
\(q+q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
|
672.2.a.i |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{3}) \) |
None |
None |
\(0\) |
\(-2\) |
\(0\) |
\(2\) |
\(-\) |
\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
|
672.2.a.j |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{3}) \) |
None |
None |
\(0\) |
\(2\) |
\(0\) |
\(-2\) |
\(-\) |
\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
|
672.2.b.a |
\(8\) |
\(5.366\) |
8.0.836829184.2 |
None |
None |
\(0\) |
\(-8\) |
\(0\) |
\(-4\) |
|
\(q-q^{3}+\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
|
672.2.b.b |
\(8\) |
\(5.366\) |
8.0.836829184.2 |
None |
None |
\(0\) |
\(8\) |
\(0\) |
\(4\) |
|
\(q+q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
|
672.2.c.a |
\(4\) |
\(5.366\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(4\) |
|
\(q-\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}+q^{7}+\cdots\)
|
672.2.c.b |
\(8\) |
\(5.366\) |
8.0.386672896.3 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q+\beta _{2}q^{3}+\beta _{1}q^{5}-q^{7}-q^{9}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)
|
672.2.h.a |
\(4\) |
\(5.366\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
|
\(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
|
672.2.h.b |
\(4\) |
\(5.366\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-3\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
|
672.2.h.c |
\(4\) |
\(5.366\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
|
672.2.h.d |
\(4\) |
\(5.366\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
|
\(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
|
672.2.h.e |
\(8\) |
\(5.366\) |
8.0.40960000.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{2}q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(-2+\beta _{6}+\cdots)q^{9}+\cdots\)
|
672.2.i.a |
\(4\) |
\(5.366\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
None |
\(0\) |
\(-4\) |
\(0\) |
\(8\) |
|
\(q+(-1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
|
672.2.i.b |
\(4\) |
\(5.366\) |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
\(\Q(\sqrt{-6}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
|
\(q+\beta _{2}q^{3}+2\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
|
672.2.i.c |
\(4\) |
\(5.366\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
None |
\(0\) |
\(4\) |
\(0\) |
\(8\) |
|
\(q+(1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
|
672.2.i.d |
\(8\) |
\(5.366\) |
8.0.3317760000.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q+(-\beta _{2}-\beta _{3})q^{3}-\beta _{3}q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
|
672.2.i.e |
\(8\) |
\(5.366\) |
8.0.\(\cdots\).11 |
\(\Q(\sqrt{-14}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{3}+(\beta _{6}-\beta _{7})q^{5}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)
|
672.2.j.a |
\(4\) |
\(5.366\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
|
\(q+(-1-\zeta_{8}^{2})q^{3}-2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+\cdots\)
|
672.2.j.b |
\(4\) |
\(5.366\) |
\(\Q(i, \sqrt{5})\) |
None |
None |
\(0\) |
\(2\) |
\(-4\) |
\(0\) |
|
\(q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
|
672.2.j.c |
\(4\) |
\(5.366\) |
\(\Q(i, \sqrt{5})\) |
None |
None |
\(0\) |
\(2\) |
\(4\) |
\(0\) |
|
\(q+(-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
|
672.2.j.d |
\(12\) |
\(5.366\) |
12.0.\(\cdots\).2 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{3}q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\beta _{1}q^{7}+\cdots\)
|
672.2.k.a |
\(8\) |
\(5.366\) |
8.0.342102016.5 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
|
\(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
|
672.2.k.b |
\(8\) |
\(5.366\) |
8.0.49787136.1 |
\(\Q(\sqrt{-21}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{1}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}-3q^{9}+\beta _{3}q^{11}+\cdots\)
|
672.2.k.c |
\(8\) |
\(5.366\) |
8.0.40960000.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\beta _{4}+\beta _{5})q^{3}+\beta _{7}q^{5}+(-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
|
672.2.k.d |
\(8\) |
\(5.366\) |
8.0.342102016.5 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(4\) |
|
\(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(1+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
|
672.2.p.a |
\(16\) |
\(5.366\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{4}q^{3}+\beta _{2}q^{5}+\beta _{7}q^{7}-q^{9}+\beta _{3}q^{11}+\cdots\)
|
672.2.q.a |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(-3\) |
\(1\) |
|
\(q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
|
672.2.q.b |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(-1\) |
\(-5\) |
|
\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
|
672.2.q.c |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(0\) |
\(1\) |
|
\(q+(-1+\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
|
672.2.q.d |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(0\) |
\(5\) |
|
\(q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
|
672.2.q.e |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(4\) |
\(5\) |
|
\(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
|
672.2.q.f |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(1\) |
\(-3\) |
\(-1\) |
|
\(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
|
672.2.q.g |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(1\) |
\(-1\) |
\(5\) |
|
\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
|
672.2.q.h |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(1\) |
\(0\) |
\(-5\) |
|
\(q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
|
672.2.q.i |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(1\) |
\(0\) |
\(-1\) |
|
\(q+(1-\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
|
672.2.q.j |
\(2\) |
\(5.366\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(1\) |
\(4\) |
\(-5\) |
|
\(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
|
672.2.q.k |
\(6\) |
\(5.366\) |
6.0.1156923.1 |
None |
None |
\(0\) |
\(-3\) |
\(0\) |
\(-3\) |
|
\(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
|
672.2.q.l |
\(6\) |
\(5.366\) |
6.0.1156923.1 |
None |
None |
\(0\) |
\(3\) |
\(0\) |
\(3\) |
|
\(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
|
672.2.bb.a |
\(32\) |
\(5.366\) |
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
672.2.bc.a |
\(4\) |
\(5.366\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
|
672.2.bc.b |
\(4\) |
\(5.366\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}+(2\zeta_{12}+\cdots)q^{7}+\cdots\)
|