78.2.a.a |
\(1\) |
\(0.623\) |
\(\Q\) |
None |
\(-1\) |
\(-1\) |
\(2\) |
\(4\) |
\(-\) |
\(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
|
78.2.b.a |
\(2\) |
\(0.623\) |
\(\Q(\sqrt{-1}) \) |
None |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
|
\(q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
|
78.2.e.a |
\(2\) |
\(0.623\) |
\(\Q(\sqrt{-3}) \) |
None |
\(1\) |
\(-1\) |
\(6\) |
\(-2\) |
|
\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
78.2.e.b |
\(2\) |
\(0.623\) |
\(\Q(\sqrt{-3}) \) |
None |
\(1\) |
\(1\) |
\(-2\) |
\(2\) |
|
\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
78.2.g.a |
\(12\) |
\(0.623\) |
12.0.\(\cdots\).52 |
None |
\(0\) |
\(0\) |
\(0\) |
\(-12\) |
|
\(q+\beta _{2}q^{2}-\beta _{4}q^{3}+\beta _{8}q^{4}+(-\beta _{1}-\beta _{11})q^{5}+\cdots\)
|
78.2.i.a |
\(4\) |
\(0.623\) |
\(\Q(\zeta_{12})\) |
None |
\(0\) |
\(-2\) |
\(0\) |
\(6\) |
|
\(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
|
78.2.i.b |
\(4\) |
\(0.623\) |
\(\Q(\zeta_{12})\) |
None |
\(0\) |
\(2\) |
\(0\) |
\(-6\) |
|
\(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
|
78.2.k.a |
\(16\) |
\(0.623\) |
16.0.\(\cdots\).9 |
None |
\(0\) |
\(0\) |
\(0\) |
\(8\) |
|
\(q+(-\beta _{7}-\beta _{15})q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
|
78.3.c.a |
\(8\) |
\(2.125\) |
8.0.\(\cdots\).2 |
None |
\(0\) |
\(0\) |
\(0\) |
\(-8\) |
|
\(q-\beta _{2}q^{2}+\beta _{4}q^{3}-2q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
|
78.3.d.a |
\(4\) |
\(2.125\) |
\(\Q(\sqrt{2}, \sqrt{-5})\) |
None |
\(0\) |
\(-8\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(-2-\beta _{3})q^{3}+2q^{4}+3\beta _{1}q^{5}+\cdots\)
|
78.3.d.b |
\(4\) |
\(2.125\) |
\(\Q(\sqrt{2}, \sqrt{-5})\) |
None |
\(0\) |
\(8\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{3}+2q^{4}-\beta _{1}q^{5}+\cdots\)
|
78.3.f.a |
\(4\) |
\(2.125\) |
\(\Q(\zeta_{12})\) |
None |
\(4\) |
\(0\) |
\(12\) |
\(-4\) |
|
\(q+(1+\zeta_{12})q^{2}+\zeta_{12}^{3}q^{3}+2\zeta_{12}q^{4}+\cdots\)
|
78.3.f.b |
\(8\) |
\(2.125\) |
8.0.\(\cdots\).1 |
None |
\(-8\) |
\(0\) |
\(0\) |
\(4\) |
|
\(q+(-1-\beta _{6})q^{2}+\beta _{1}q^{3}+2\beta _{6}q^{4}+\cdots\)
|
78.3.h.a |
\(8\) |
\(2.125\) |
8.0.4857532416.2 |
None |
\(0\) |
\(-2\) |
\(0\) |
\(-12\) |
|
\(q+\beta _{2}q^{2}+(-1-\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
|
78.3.h.b |
\(12\) |
\(2.125\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
\(0\) |
\(2\) |
\(0\) |
\(22\) |
|
\(q+\beta _{7}q^{2}+(-\beta _{4}+\beta _{9})q^{3}+2\beta _{1}q^{4}+\cdots\)
|
78.3.j.a |
\(20\) |
\(2.125\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(18\) |
|
\(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-2-2\beta _{6})q^{4}+\cdots\)
|
78.3.l.a |
\(4\) |
\(2.125\) |
\(\Q(\zeta_{12})\) |
None |
\(-2\) |
\(0\) |
\(-12\) |
\(-10\) |
|
\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)
|
78.3.l.b |
\(4\) |
\(2.125\) |
\(\Q(\zeta_{12})\) |
None |
\(2\) |
\(0\) |
\(6\) |
\(20\) |
|
\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
|
78.3.l.c |
\(8\) |
\(2.125\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(4\) |
\(0\) |
\(-6\) |
\(10\) |
|
\(q+(-\beta _{4}-\beta _{5})q^{2}+(2\beta _{2}-\beta _{5})q^{3}+(2\beta _{2}+\cdots)q^{4}+\cdots\)
|
78.4.a.a |
\(1\) |
\(4.602\) |
\(\Q\) |
None |
\(-2\) |
\(-3\) |
\(-16\) |
\(28\) |
\(+\) |
\(q-2q^{2}-3q^{3}+4q^{4}-2^{4}q^{5}+6q^{6}+\cdots\)
|
78.4.a.b |
\(1\) |
\(4.602\) |
\(\Q\) |
None |
\(-2\) |
\(3\) |
\(-16\) |
\(-8\) |
\(-\) |
\(q-2q^{2}+3q^{3}+4q^{4}-2^{4}q^{5}-6q^{6}+\cdots\)
|
78.4.a.c |
\(1\) |
\(4.602\) |
\(\Q\) |
None |
\(-2\) |
\(3\) |
\(10\) |
\(-8\) |
\(+\) |
\(q-2q^{2}+3q^{3}+4q^{4}+10q^{5}-6q^{6}+\cdots\)
|
78.4.a.d |
\(1\) |
\(4.602\) |
\(\Q\) |
None |
\(2\) |
\(-3\) |
\(-20\) |
\(-32\) |
\(-\) |
\(q+2q^{2}-3q^{3}+4q^{4}-20q^{5}-6q^{6}+\cdots\)
|
78.4.a.e |
\(1\) |
\(4.602\) |
\(\Q\) |
None |
\(2\) |
\(-3\) |
\(6\) |
\(20\) |
\(+\) |
\(q+2q^{2}-3q^{3}+4q^{4}+6q^{5}-6q^{6}+\cdots\)
|
78.4.a.f |
\(1\) |
\(4.602\) |
\(\Q\) |
None |
\(2\) |
\(3\) |
\(4\) |
\(4\) |
\(+\) |
\(q+2q^{2}+3q^{3}+4q^{4}+4q^{5}+6q^{6}+\cdots\)
|
78.4.b.a |
\(2\) |
\(4.602\) |
\(\Q(\sqrt{-1}) \) |
None |
\(0\) |
\(-6\) |
\(0\) |
\(0\) |
|
\(q+iq^{2}-3q^{3}-4q^{4}-4iq^{5}-3iq^{6}+\cdots\)
|
78.4.b.b |
\(4\) |
\(4.602\) |
\(\Q(i, \sqrt{17})\) |
None |
\(0\) |
\(12\) |
\(0\) |
\(0\) |
|
\(q-\beta _{1}q^{2}+3q^{3}-4q^{4}+(4\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
|
78.4.e.a |
\(2\) |
\(4.602\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-2\) |
\(3\) |
\(14\) |
\(-16\) |
|
\(q+(-2+2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
|
78.4.e.b |
\(4\) |
\(4.602\) |
\(\Q(\sqrt{-3}, \sqrt{673})\) |
None |
\(-4\) |
\(-6\) |
\(26\) |
\(-9\) |
|
\(q+(-2+2\beta _{2})q^{2}+(-3+3\beta _{2})q^{3}+\cdots\)
|
78.4.e.c |
\(4\) |
\(4.602\) |
\(\Q(\sqrt{-3}, \sqrt{61})\) |
None |
\(4\) |
\(6\) |
\(4\) |
\(-18\) |
|
\(q+(2-2\beta _{1})q^{2}+(3-3\beta _{1})q^{3}-4\beta _{1}q^{4}+\cdots\)
|
78.4.e.d |
\(6\) |
\(4.602\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(6\) |
\(-9\) |
\(-24\) |
\(17\) |
|
\(q+(2+2\beta _{2})q^{2}+(-3-3\beta _{2})q^{3}+4\beta _{2}q^{4}+\cdots\)
|
78.4.g.a |
\(28\) |
\(4.602\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(20\) |
|
|
78.4.i.a |
\(4\) |
\(4.602\) |
\(\Q(\zeta_{12})\) |
None |
\(0\) |
\(-6\) |
\(0\) |
\(-42\) |
|
\(q+2\zeta_{12}q^{2}+(-3+3\zeta_{12}^{2})q^{3}+4\zeta_{12}^{2}q^{4}+\cdots\)
|
78.4.i.b |
\(8\) |
\(4.602\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(0\) |
\(12\) |
\(0\) |
\(24\) |
|
\(q-\beta _{4}q^{2}+3\beta _{1}q^{3}+(4-4\beta _{1})q^{4}+(3+\cdots)q^{5}+\cdots\)
|
78.4.k.a |
\(56\) |
\(4.602\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(-92\) |
|
|
78.5.c.a |
\(16\) |
\(8.063\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(0\) |
\(12\) |
\(0\) |
\(80\) |
|
\(q+\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4})q^{3}-8q^{4}+\cdots\)
|
78.5.d.a |
\(20\) |
\(8.063\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(-2\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
|
78.5.f.a |
\(8\) |
\(8.063\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(-16\) |
\(0\) |
\(-36\) |
\(-8\) |
|
\(q+(-2+2\beta _{2})q^{2}-3\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots\)
|
78.5.f.b |
\(8\) |
\(8.063\) |
8.0.\(\cdots\).2 |
None |
\(16\) |
\(0\) |
\(60\) |
\(88\) |
|
\(q+(2+2\beta _{2})q^{2}+\beta _{3}q^{3}+8\beta _{2}q^{4}+(7+\cdots)q^{5}+\cdots\)
|
78.5.h.a |
\(36\) |
\(8.063\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(-90\) |
|
|
78.5.j.a |
\(36\) |
\(8.063\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(126\) |
|
|
78.5.l.a |
\(8\) |
\(8.063\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(-8\) |
\(0\) |
\(-72\) |
\(118\) |
|
\(q+(-2-2\beta _{1}+2\beta _{4})q^{2}+(-3\beta _{4}-6\beta _{5}+\cdots)q^{3}+\cdots\)
|
78.5.l.b |
\(8\) |
\(8.063\) |
8.0.\(\cdots\).10 |
None |
\(8\) |
\(0\) |
\(-24\) |
\(22\) |
|
\(q+(2-2\beta _{1}+2\beta _{2})q^{2}+(3\beta _{2}+6\beta _{3}+\cdots)q^{3}+\cdots\)
|
78.5.l.c |
\(12\) |
\(8.063\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
\(-12\) |
\(0\) |
\(12\) |
\(48\) |
|
\(q+(-2+2\beta _{1}-2\beta _{3})q^{2}+(6\beta _{2}+3\beta _{3}+\cdots)q^{3}+\cdots\)
|
78.5.l.d |
\(12\) |
\(8.063\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
\(12\) |
\(0\) |
\(60\) |
\(-48\) |
|
\(q+(2+2\beta _{1}-2\beta _{2}-2\beta _{4})q^{2}+(-3\beta _{1}+\cdots)q^{3}+\cdots\)
|
78.6.a.a |
\(1\) |
\(12.510\) |
\(\Q\) |
None |
\(-4\) |
\(-9\) |
\(4\) |
\(-8\) |
\(+\) |
\(q-4q^{2}-9q^{3}+2^{4}q^{4}+4q^{5}+6^{2}q^{6}+\cdots\)
|
78.6.a.b |
\(1\) |
\(12.510\) |
\(\Q\) |
None |
\(-4\) |
\(9\) |
\(24\) |
\(-238\) |
\(+\) |
\(q-4q^{2}+9q^{3}+2^{4}q^{4}+24q^{5}-6^{2}q^{6}+\cdots\)
|
78.6.a.c |
\(1\) |
\(12.510\) |
\(\Q\) |
None |
\(-4\) |
\(9\) |
\(76\) |
\(100\) |
\(-\) |
\(q-4q^{2}+9q^{3}+2^{4}q^{4}+76q^{5}-6^{2}q^{6}+\cdots\)
|
78.6.a.d |
\(1\) |
\(12.510\) |
\(\Q\) |
None |
\(4\) |
\(-9\) |
\(4\) |
\(-146\) |
\(+\) |
\(q+4q^{2}-9q^{3}+2^{4}q^{4}+4q^{5}-6^{2}q^{6}+\cdots\)
|
78.6.a.e |
\(1\) |
\(12.510\) |
\(\Q\) |
None |
\(4\) |
\(-9\) |
\(56\) |
\(-68\) |
\(-\) |
\(q+4q^{2}-9q^{3}+2^{4}q^{4}+56q^{5}-6^{2}q^{6}+\cdots\)
|