1089.1.c.a |
\(2\) |
\(0.543\) |
\(\Q(\sqrt{-2}) \) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+q^{4}-\beta q^{7}+\beta q^{13}+q^{16}-\beta q^{19}+\cdots\)
|
1089.1.h.a |
\(4\) |
\(0.543\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
None |
\(0\) |
\(2\) |
\(2\) |
\(0\) |
|
\(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
|
1089.1.i.a |
\(2\) |
\(0.543\) |
\(\Q(\sqrt{-3}) \) |
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(1\) |
\(3\) |
\(0\) |
|
\(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
|
1089.1.k.a |
\(8\) |
\(0.543\) |
8.0.64000000.1 |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{4}-\beta _{7}q^{7}-\beta _{1}q^{13}+\beta _{4}q^{16}+\cdots\)
|
1089.1.r.a |
\(8\) |
\(0.543\) |
\(\Q(\zeta_{15})\) |
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(-1\) |
\(-3\) |
\(0\) |
|
\(q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{11}+\cdots)q^{5}+\cdots\)
|
1089.1.s.a |
\(8\) |
\(0.543\) |
\(\Q(\zeta_{15})\) |
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(1\) |
\(-1\) |
\(0\) |
|
\(q-\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+\zeta_{30}q^{5}+\cdots\)
|
1089.1.s.b |
\(16\) |
\(0.543\) |
16.0.\(\cdots\).1 |
None |
None |
\(0\) |
\(-2\) |
\(-2\) |
\(0\) |
|
\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots\)
|
1089.2.a.a |
\(1\) |
\(8.696\) |
\(\Q\) |
None |
None |
\(-2\) |
\(0\) |
\(-4\) |
\(-1\) |
\(+\) |
\(q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots\)
|
1089.2.a.b |
\(1\) |
\(8.696\) |
\(\Q\) |
None |
None |
\(-2\) |
\(0\) |
\(-1\) |
\(2\) |
\(+\) |
\(q-2q^{2}+2q^{4}-q^{5}+2q^{7}+2q^{10}+\cdots\)
|
1089.2.a.c |
\(1\) |
\(8.696\) |
\(\Q\) |
None |
None |
\(-1\) |
\(0\) |
\(-1\) |
\(-2\) |
\(+\) |
\(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
|
1089.2.a.d |
\(1\) |
\(8.696\) |
\(\Q\) |
None |
None |
\(-1\) |
\(0\) |
\(4\) |
\(2\) |
\(-\) |
\(q-q^{2}-q^{4}+4q^{5}+2q^{7}+3q^{8}-4q^{10}+\cdots\)
|
1089.2.a.e |
\(1\) |
\(8.696\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-5\) |
\(-\) |
\(q-2q^{4}-5q^{7}-2q^{13}+4q^{16}+7q^{19}+\cdots\)
|
1089.2.a.f |
\(1\) |
\(8.696\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(5\) |
\(-\) |
\(q-2q^{4}+5q^{7}+2q^{13}+4q^{16}-7q^{19}+\cdots\)
|
1089.2.a.g |
\(1\) |
\(8.696\) |
\(\Q\) |
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(0\) |
\(3\) |
\(0\) |
\(-\) |
\(q-2q^{4}+3q^{5}+4q^{16}-6q^{20}+9q^{23}+\cdots\)
|
1089.2.a.h |
\(1\) |
\(8.696\) |
\(\Q\) |
None |
None |
\(1\) |
\(0\) |
\(-4\) |
\(2\) |
\(-\) |
\(q+q^{2}-q^{4}-4q^{5}+2q^{7}-3q^{8}-4q^{10}+\cdots\)
|
1089.2.a.i |
\(1\) |
\(8.696\) |
\(\Q\) |
None |
None |
\(1\) |
\(0\) |
\(-1\) |
\(2\) |
\(+\) |
\(q+q^{2}-q^{4}-q^{5}+2q^{7}-3q^{8}-q^{10}+\cdots\)
|
1089.2.a.j |
\(1\) |
\(8.696\) |
\(\Q\) |
None |
None |
\(1\) |
\(0\) |
\(2\) |
\(-4\) |
\(+\) |
\(q+q^{2}-q^{4}+2q^{5}-4q^{7}-3q^{8}+2q^{10}+\cdots\)
|
1089.2.a.k |
\(1\) |
\(8.696\) |
\(\Q\) |
None |
None |
\(2\) |
\(0\) |
\(-4\) |
\(1\) |
\(+\) |
\(q+2q^{2}+2q^{4}-4q^{5}+q^{7}-8q^{10}+\cdots\)
|
1089.2.a.l |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{5}) \) |
None |
None |
\(-3\) |
\(0\) |
\(-1\) |
\(2\) |
\(+\) |
\(q+(-1-\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots\)
|
1089.2.a.m |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{5}) \) |
None |
None |
\(-1\) |
\(0\) |
\(3\) |
\(6\) |
\(-\) |
\(q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+3q^{7}+\cdots\)
|
1089.2.a.n |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{3}) \) |
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(+\) |
\(q-2q^{4}-\beta q^{7}+4\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots\)
|
1089.2.a.o |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{3}) \) |
None |
None |
\(0\) |
\(0\) |
\(6\) |
\(0\) |
\(-\) |
\(q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots\)
|
1089.2.a.p |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{5}) \) |
None |
None |
\(0\) |
\(0\) |
\(-4\) |
\(0\) |
\(-\) |
\(q-\beta q^{2}+3q^{4}-2q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
|
1089.2.a.q |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{7}) \) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
\(-\) |
\(q+\beta q^{2}+5q^{4}+\beta q^{5}-2q^{7}+3\beta q^{8}+\cdots\)
|
1089.2.a.r |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{7}) \) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(4\) |
\(-\) |
\(q+\beta q^{2}+5q^{4}-\beta q^{5}+2q^{7}+3\beta q^{8}+\cdots\)
|
1089.2.a.s |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{5}) \) |
None |
None |
\(1\) |
\(0\) |
\(3\) |
\(-6\) |
\(+\) |
\(q+\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}-3q^{7}+\cdots\)
|
1089.2.a.t |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{5}) \) |
None |
None |
\(3\) |
\(0\) |
\(-1\) |
\(-2\) |
\(-\) |
\(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots\)
|
1089.2.a.u |
\(4\) |
\(8.696\) |
\(\Q(\sqrt{3}, \sqrt{11})\) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
\(-\) |
\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
|
1089.2.a.v |
\(4\) |
\(8.696\) |
4.4.4400.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
\(+\) |
\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}+(-3+\cdots)q^{7}+\cdots\)
|
1089.2.a.w |
\(4\) |
\(8.696\) |
4.4.4400.1 |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(8\) |
\(-\) |
\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{1}q^{5}+(3+2\beta _{2}+\cdots)q^{7}+\cdots\)
|
1089.2.d.a |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{-2}) \) |
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-q^{2}-q^{4}-\beta q^{5}-2\beta q^{7}+3q^{8}+\cdots\)
|
1089.2.d.b |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{-2}) \) |
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+q^{2}-q^{4}+\beta q^{5}-2\beta q^{7}-3q^{8}+\cdots\)
|
1089.2.d.c |
\(4\) |
\(8.696\) |
\(\Q(\sqrt{-2}, \sqrt{3})\) |
None |
None |
\(-4\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-1-\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots\)
|
1089.2.d.d |
\(4\) |
\(8.696\) |
\(\Q(\sqrt{-2}, \sqrt{3})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{2}+q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots\)
|
1089.2.d.e |
\(4\) |
\(8.696\) |
\(\Q(\sqrt{-2}, \sqrt{3})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{2}q^{2}+q^{4}+(2\beta _{1}-\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots\)
|
1089.2.d.f |
\(4\) |
\(8.696\) |
\(\Q(\sqrt{-2}, \sqrt{3})\) |
None |
None |
\(4\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(1+\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots\)
|
1089.2.d.g |
\(16\) |
\(8.696\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{15}q^{2}+(1+\beta _{4})q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
|
1089.2.e.a |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(-2\) |
\(0\) |
\(2\) |
\(4\) |
|
\(q+(-2+2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
|
1089.2.e.b |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-3\) |
\(3\) |
\(-4\) |
|
\(q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
|
1089.2.e.c |
\(2\) |
\(8.696\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(1\) |
\(-3\) |
\(-1\) |
\(4\) |
|
\(q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
|
1089.2.e.d |
\(4\) |
\(8.696\) |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
None |
None |
\(-3\) |
\(-6\) |
\(-2\) |
\(-2\) |
|
\(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots\)
|
1089.2.e.e |
\(4\) |
\(8.696\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(0\) |
\(-6\) |
\(6\) |
\(0\) |
|
\(q-\zeta_{12}^{2}q^{2}+(-1-\zeta_{12})q^{3}+(-1+\cdots)q^{4}+\cdots\)
|
1089.2.e.f |
\(4\) |
\(8.696\) |
\(\Q(\sqrt{-3}, \sqrt{-11})\) |
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(1\) |
\(-3\) |
\(0\) |
|
\(q-\beta _{3}q^{3}+2\beta _{2}q^{4}+(1-2\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
|
1089.2.e.g |
\(4\) |
\(8.696\) |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
None |
None |
\(3\) |
\(-6\) |
\(-2\) |
\(2\) |
|
\(q+(1+\beta _{1}+\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots\)
|
1089.2.e.h |
\(6\) |
\(8.696\) |
\(\Q(\zeta_{18})\) |
None |
None |
\(0\) |
\(0\) |
\(-3\) |
\(-3\) |
|
\(q+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
|
1089.2.e.i |
\(8\) |
\(8.696\) |
8.0.508277025.1 |
None |
None |
\(1\) |
\(5\) |
\(-4\) |
\(1\) |
|
\(q+(\beta _{2}+\beta _{7})q^{2}+(1+\beta _{7})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
|
1089.2.e.j |
\(12\) |
\(8.696\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
None |
\(0\) |
\(4\) |
\(2\) |
\(0\) |
|
\(q+\beta _{7}q^{2}+(1+\beta _{2}-\beta _{6})q^{3}+(-1-2\beta _{4}+\cdots)q^{4}+\cdots\)
|
1089.2.e.k |
\(16\) |
\(8.696\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
None |
\(0\) |
\(-2\) |
\(4\) |
\(0\) |
|
\(q+(-\beta _{1}-\beta _{2}-\beta _{6})q^{2}-\beta _{13}q^{3}+(2\beta _{5}+\cdots)q^{4}+\cdots\)
|
1089.2.e.l |
\(20\) |
\(8.696\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
None |
\(0\) |
\(-1\) |
\(-3\) |
\(1\) |
|
\(q-\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots\)
|
1089.2.e.m |
\(20\) |
\(8.696\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
None |
\(0\) |
\(-1\) |
\(-3\) |
\(-1\) |
|
\(q+\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots\)
|