304.1.e.a |
\(1\) |
\(0.152\) |
\(\Q\) |
\(\Q(\sqrt{-19}) \) |
None |
\(0\) |
\(0\) |
\(-1\) |
\(1\) |
|
\(q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
|
304.2.a.a |
\(1\) |
\(2.427\) |
\(\Q\) |
None |
None |
\(0\) |
\(-2\) |
\(-1\) |
\(3\) |
\(+\) |
\(q-2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
|
304.2.a.b |
\(1\) |
\(2.427\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(0\) |
\(-3\) |
\(+\) |
\(q-q^{3}-3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
|
304.2.a.c |
\(1\) |
\(2.427\) |
\(\Q\) |
None |
None |
\(0\) |
\(-1\) |
\(0\) |
\(1\) |
\(-\) |
\(q-q^{3}+q^{7}-2q^{9}+6q^{11}+5q^{13}+\cdots\)
|
304.2.a.d |
\(1\) |
\(2.427\) |
\(\Q\) |
None |
None |
\(0\) |
\(1\) |
\(-4\) |
\(-3\) |
\(+\) |
\(q+q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
|
304.2.a.e |
\(1\) |
\(2.427\) |
\(\Q\) |
None |
None |
\(0\) |
\(2\) |
\(-1\) |
\(3\) |
\(-\) |
\(q+2q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
|
304.2.a.f |
\(1\) |
\(2.427\) |
\(\Q\) |
None |
None |
\(0\) |
\(2\) |
\(3\) |
\(1\) |
\(-\) |
\(q+2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
|
304.2.a.g |
\(3\) |
\(2.427\) |
3.3.961.1 |
None |
None |
\(0\) |
\(-1\) |
\(1\) |
\(-4\) |
\(-\) |
\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
|
304.2.h.a |
\(2\) |
\(2.427\) |
\(\Q(\sqrt{-19}) \) |
\(\Q(\sqrt{-19}) \) |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
|
304.2.h.b |
\(4\) |
\(2.427\) |
\(\Q(\sqrt{-3}, \sqrt{7})\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
|
304.2.h.c |
\(4\) |
\(2.427\) |
\(\Q(\sqrt{-3}, \sqrt{-19})\) |
\(\Q(\sqrt{-19}) \) |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
|
304.2.i.a |
\(2\) |
\(2.427\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(1\) |
\(0\) |
|
\(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
|
304.2.i.b |
\(2\) |
\(2.427\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(1\) |
\(-3\) |
\(0\) |
|
\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
|
304.2.i.c |
\(2\) |
\(2.427\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(1\) |
\(0\) |
\(8\) |
|
\(q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots\)
|
304.2.i.d |
\(2\) |
\(2.427\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(1\) |
\(4\) |
\(0\) |
|
\(q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
|
304.2.i.e |
\(4\) |
\(2.427\) |
\(\Q(\sqrt{-3}, \sqrt{7})\) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(-4\) |
|
\(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
|
304.2.i.f |
\(6\) |
\(2.427\) |
6.0.2696112.1 |
None |
None |
\(0\) |
\(1\) |
\(-1\) |
\(4\) |
|
\(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
|
304.2.k.a |
\(4\) |
\(2.427\) |
\(\Q(\zeta_{8})\) |
None |
None |
\(0\) |
\(-4\) |
\(-8\) |
\(0\) |
|
\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
|
304.2.k.b |
\(68\) |
\(2.427\) |
|
None |
None |
\(0\) |
\(4\) |
\(8\) |
\(0\) |
|
|
304.2.m.a |
\(76\) |
\(2.427\) |
|
None |
None |
\(0\) |
\(0\) |
\(-4\) |
\(-8\) |
|
|
304.2.n.a |
\(2\) |
\(2.427\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(-1\) |
\(-3\) |
\(0\) |
|
\(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
|
304.2.n.b |
\(2\) |
\(2.427\) |
\(\Q(\sqrt{-3}) \) |
None |
None |
\(0\) |
\(1\) |
\(-3\) |
\(0\) |
|
\(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
|
304.2.n.c |
\(4\) |
\(2.427\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
|
\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots\)
|
304.2.n.d |
\(6\) |
\(2.427\) |
6.0.31726512.1 |
None |
None |
\(0\) |
\(-1\) |
\(2\) |
\(0\) |
|
\(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
|
304.2.n.e |
\(6\) |
\(2.427\) |
6.0.31726512.1 |
None |
None |
\(0\) |
\(1\) |
\(2\) |
\(0\) |
|
\(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
|
304.2.u.a |
\(6\) |
\(2.427\) |
\(\Q(\zeta_{18})\) |
None |
None |
\(0\) |
\(-9\) |
\(-6\) |
\(-6\) |
|
\(q+(-1+\zeta_{18}-2\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots\)
|
304.2.u.b |
\(6\) |
\(2.427\) |
\(\Q(\zeta_{18})\) |
None |
None |
\(0\) |
\(3\) |
\(-6\) |
\(0\) |
|
\(q+(1-\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+(-1+\cdots)q^{5}+\cdots\)
|
304.2.u.c |
\(6\) |
\(2.427\) |
\(\Q(\zeta_{18})\) |
None |
None |
\(0\) |
\(3\) |
\(0\) |
\(6\) |
|
\(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+2\zeta_{18}^{4}q^{5}+\cdots\)
|
304.2.u.d |
\(6\) |
\(2.427\) |
\(\Q(\zeta_{18})\) |
None |
None |
\(0\) |
\(6\) |
\(6\) |
\(-3\) |
|
\(q+(1+\zeta_{18}^{2})q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{5})q^{5}+\cdots\)
|
304.2.u.e |
\(12\) |
\(2.427\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
None |
\(0\) |
\(3\) |
\(0\) |
\(-3\) |
|
\(q+(1+\beta _{5}-\beta _{7}-\beta _{9}-\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots\)
|
304.2.u.f |
\(18\) |
\(2.427\) |
\(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(9\) |
|
\(q+(-\beta _{2}+\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
|
304.2.v.a |
\(152\) |
\(2.427\) |
|
None |
None |
\(-2\) |
\(-2\) |
\(-2\) |
\(0\) |
|
|
304.2.x.a |
\(4\) |
\(2.427\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(-2\) |
\(2\) |
\(-2\) |
\(-4\) |
|
\(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
|
304.2.x.b |
\(4\) |
\(2.427\) |
\(\Q(\zeta_{12})\) |
None |
None |
\(2\) |
\(4\) |
\(-2\) |
\(-4\) |
|
\(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
|
304.2.x.c |
\(144\) |
\(2.427\) |
|
None |
None |
\(-6\) |
\(-12\) |
\(2\) |
\(-8\) |
|
|
304.2.be.a |
\(12\) |
\(2.427\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
|
304.2.be.b |
\(12\) |
\(2.427\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots\)
|
304.2.be.c |
\(18\) |
\(2.427\) |
\(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-9\) |
|
\(q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
|
304.2.be.d |
\(18\) |
\(2.427\) |
\(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(9\) |
|
\(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
|
304.2.bg.a |
\(456\) |
\(2.427\) |
|
None |
None |
\(-12\) |
\(-12\) |
\(-12\) |
\(-12\) |
|
|
304.2.bi.a |
\(456\) |
\(2.427\) |
|
None |
None |
\(-12\) |
\(-12\) |
\(-12\) |
\(0\) |
|
|
304.3.d.a |
\(6\) |
\(8.283\) |
6.0.210056875.1 |
None |
None |
\(0\) |
\(0\) |
\(14\) |
\(0\) |
|
\(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+(-\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots\)
|
304.3.d.b |
\(12\) |
\(8.283\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(0\) |
|
\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-1+\cdots)q^{9}+\cdots\)
|
304.3.e.a |
\(1\) |
\(8.283\) |
\(\Q\) |
\(\Q(\sqrt{-19}) \) |
None |
\(0\) |
\(0\) |
\(-9\) |
\(5\) |
|
\(q-9q^{5}+5q^{7}+9q^{9}-3q^{11}+15q^{17}+\cdots\)
|
304.3.e.b |
\(2\) |
\(8.283\) |
\(\Q(\sqrt{-29}) \) |
None |
None |
\(0\) |
\(0\) |
\(-8\) |
\(2\) |
|
\(q+\beta q^{3}-4q^{5}+q^{7}-20q^{9}-14q^{11}+\cdots\)
|
304.3.e.c |
\(2\) |
\(8.283\) |
\(\Q(\sqrt{-2}) \) |
None |
None |
\(0\) |
\(0\) |
\(-2\) |
\(-10\) |
|
\(q+\beta q^{3}-q^{5}-5q^{7}+q^{9}-5q^{11}+\cdots\)
|
304.3.e.d |
\(2\) |
\(8.283\) |
\(\Q(\sqrt{-13}) \) |
None |
None |
\(0\) |
\(0\) |
\(8\) |
\(10\) |
|
\(q+\beta q^{3}+4q^{5}+5q^{7}-4q^{9}+10q^{11}+\cdots\)
|
304.3.e.e |
\(2\) |
\(8.283\) |
\(\Q(\sqrt{57}) \) |
\(\Q(\sqrt{-19}) \) |
None |
\(0\) |
\(0\) |
\(9\) |
\(-5\) |
|
\(q+(5-\beta )q^{5}+(-1-3\beta )q^{7}+9q^{9}+\cdots\)
|
304.3.e.f |
\(2\) |
\(8.283\) |
\(\Q(\sqrt{-2}) \) |
None |
None |
\(0\) |
\(0\) |
\(14\) |
\(-22\) |
|
\(q+\beta q^{3}+7q^{5}-11q^{7}-23q^{9}-3q^{11}+\cdots\)
|
304.3.e.g |
\(8\) |
\(8.283\) |
\(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
None |
None |
\(0\) |
\(0\) |
\(-14\) |
\(6\) |
|
\(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(1-\beta _{3})q^{7}+\cdots\)
|