38.2.a.a |
\(1\) |
\(0.303\) |
\(\Q\) |
None |
\(-1\) |
\(1\) |
\(0\) |
\(-1\) |
\(-\) |
\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
|
38.2.a.b |
\(1\) |
\(0.303\) |
\(\Q\) |
None |
\(1\) |
\(-1\) |
\(-4\) |
\(3\) |
\(-\) |
\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots\)
|
38.2.c.a |
\(2\) |
\(0.303\) |
\(\Q(\sqrt{-3}) \) |
None |
\(1\) |
\(-1\) |
\(0\) |
\(-8\) |
|
\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
|
38.2.c.b |
\(4\) |
\(0.303\) |
\(\Q(\sqrt{-3}, \sqrt{7})\) |
None |
\(-2\) |
\(0\) |
\(-2\) |
\(4\) |
|
\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
|
38.2.e.a |
\(6\) |
\(0.303\) |
\(\Q(\zeta_{18})\) |
None |
\(0\) |
\(-3\) |
\(0\) |
\(-6\) |
|
\(q-\zeta_{18}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{2}q^{4}+\cdots\)
|
38.3.b.a |
\(2\) |
\(1.035\) |
\(\Q(\sqrt{-2}) \) |
None |
\(0\) |
\(0\) |
\(-2\) |
\(10\) |
|
\(q+\beta q^{2}+2\beta q^{3}-2q^{4}-q^{5}-4q^{6}+\cdots\)
|
38.3.d.a |
\(4\) |
\(1.035\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
None |
\(0\) |
\(6\) |
\(2\) |
\(8\) |
|
\(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
|
38.3.f.a |
\(24\) |
\(1.035\) |
|
None |
\(0\) |
\(-6\) |
\(0\) |
\(-18\) |
|
|
38.4.a.a |
\(1\) |
\(2.242\) |
\(\Q\) |
None |
\(-2\) |
\(-2\) |
\(-9\) |
\(-31\) |
\(-\) |
\(q-2q^{2}-2q^{3}+4q^{4}-9q^{5}+4q^{6}+\cdots\)
|
38.4.a.b |
\(2\) |
\(2.242\) |
\(\Q(\sqrt{177}) \) |
None |
\(-4\) |
\(1\) |
\(10\) |
\(57\) |
\(+\) |
\(q-2q^{2}+(1-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)
|
38.4.a.c |
\(2\) |
\(2.242\) |
\(\Q(\sqrt{73}) \) |
None |
\(4\) |
\(9\) |
\(-9\) |
\(-18\) |
\(+\) |
\(q+2q^{2}+(5-\beta )q^{3}+4q^{4}+(-6+3\beta )q^{5}+\cdots\)
|
38.4.c.a |
\(2\) |
\(2.242\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-2\) |
\(-5\) |
\(-3\) |
\(-64\) |
|
\(q+(-2+2\zeta_{6})q^{2}+(-5+5\zeta_{6})q^{3}+\cdots\)
|
38.4.c.b |
\(2\) |
\(2.242\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-2\) |
\(5\) |
\(12\) |
\(16\) |
|
\(q+(-2+2\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
|
38.4.c.c |
\(6\) |
\(2.242\) |
\(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
None |
\(6\) |
\(-5\) |
\(-1\) |
\(52\) |
|
\(q+(2-2\beta _{4})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{4}+\cdots)q^{3}+\cdots\)
|
38.4.e.a |
\(12\) |
\(2.242\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
\(0\) |
\(-9\) |
\(0\) |
\(21\) |
|
\(q-2\beta _{3}q^{2}+(-1+2\beta _{2}-\beta _{4}+2\beta _{6}+\cdots)q^{3}+\cdots\)
|
38.4.e.b |
\(18\) |
\(2.242\) |
\(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
None |
\(0\) |
\(6\) |
\(0\) |
\(-33\) |
|
\(q-2\beta _{8}q^{2}+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{9})q^{3}+\cdots\)
|
38.5.b.a |
\(8\) |
\(3.928\) |
\(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(18\) |
\(-162\) |
|
\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-8q^{4}+(2-\beta _{6}+\cdots)q^{5}+\cdots\)
|
38.5.d.a |
\(16\) |
\(3.928\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(0\) |
\(-12\) |
\(-18\) |
\(72\) |
|
\(q+(-\beta _{5}+\beta _{9})q^{2}+(-1+\beta _{3})q^{3}+8\beta _{7}q^{4}+\cdots\)
|
38.5.f.a |
\(36\) |
\(3.928\) |
|
None |
\(0\) |
\(12\) |
\(0\) |
\(90\) |
|
|
38.6.a.a |
\(1\) |
\(6.095\) |
\(\Q\) |
None |
\(-4\) |
\(-6\) |
\(31\) |
\(-27\) |
\(+\) |
\(q-4q^{2}-6q^{3}+2^{4}q^{4}+31q^{5}+24q^{6}+\cdots\)
|
38.6.a.b |
\(1\) |
\(6.095\) |
\(\Q\) |
None |
\(4\) |
\(-14\) |
\(-45\) |
\(-121\) |
\(+\) |
\(q+4q^{2}-14q^{3}+2^{4}q^{4}-45q^{5}-56q^{6}+\cdots\)
|
38.6.a.c |
\(2\) |
\(6.095\) |
\(\Q(\sqrt{1441}) \) |
None |
\(-8\) |
\(3\) |
\(-45\) |
\(114\) |
\(-\) |
\(q-4q^{2}+(2-\beta )q^{3}+2^{4}q^{4}+(-21+\cdots)q^{5}+\cdots\)
|
38.6.a.d |
\(3\) |
\(6.095\) |
\(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
None |
\(12\) |
\(13\) |
\(81\) |
\(228\) |
\(-\) |
\(q+4q^{2}+(4+\beta _{1})q^{3}+2^{4}q^{4}+(3^{3}-\beta _{1}+\cdots)q^{5}+\cdots\)
|
38.6.c.a |
\(6\) |
\(6.095\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(12\) |
\(-15\) |
\(14\) |
\(-624\) |
|
\(q+(4-4\beta _{3})q^{2}+(-5+\beta _{1}+\beta _{2}+5\beta _{3}+\cdots)q^{3}+\cdots\)
|
38.6.c.b |
\(8\) |
\(6.095\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(-16\) |
\(-14\) |
\(-36\) |
\(76\) |
|
\(q+(-4+4\beta _{2})q^{2}+(-3+3\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
|
38.6.e.a |
\(24\) |
\(6.095\) |
|
None |
\(0\) |
\(18\) |
\(0\) |
\(438\) |
|
|
38.6.e.b |
\(30\) |
\(6.095\) |
|
None |
\(0\) |
\(15\) |
\(0\) |
\(-84\) |
|
|
38.7.b.a |
\(10\) |
\(8.742\) |
\(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(-112\) |
\(-224\) |
|
\(q-\beta _{6}q^{2}+(\beta _{5}+\beta _{6})q^{3}-2^{5}q^{4}+(-11+\cdots)q^{5}+\cdots\)
|
38.7.d.a |
\(20\) |
\(8.742\) |
\(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
None |
\(0\) |
\(-30\) |
\(112\) |
\(-208\) |
|
\(q-\beta _{8}q^{2}+(-2+\beta _{2}+\beta _{6})q^{3}+(2^{5}+\cdots)q^{4}+\cdots\)
|
38.7.f.a |
\(60\) |
\(8.742\) |
|
None |
\(0\) |
\(30\) |
\(0\) |
\(432\) |
|
|
38.8.a.a |
\(1\) |
\(11.871\) |
\(\Q\) |
None |
\(-8\) |
\(77\) |
\(440\) |
\(951\) |
\(+\) |
\(q-8q^{2}+77q^{3}+2^{6}q^{4}+440q^{5}+\cdots\)
|
38.8.a.b |
\(2\) |
\(11.871\) |
\(\Q(\sqrt{2737}) \) |
None |
\(-16\) |
\(-61\) |
\(175\) |
\(-2592\) |
\(+\) |
\(q-8q^{2}+(-30-\beta )q^{3}+2^{6}q^{4}+(95+\cdots)q^{5}+\cdots\)
|
38.8.a.c |
\(2\) |
\(11.871\) |
\(\Q(\sqrt{17953}) \) |
None |
\(-16\) |
\(-11\) |
\(-69\) |
\(-348\) |
\(-\) |
\(q-8q^{2}+(-5-\beta )q^{3}+2^{6}q^{4}+(-6^{2}+\cdots)q^{5}+\cdots\)
|
38.8.a.d |
\(2\) |
\(11.871\) |
\(\Q(\sqrt{633}) \) |
None |
\(16\) |
\(-69\) |
\(155\) |
\(-2238\) |
\(-\) |
\(q+8q^{2}+(-33-3\beta )q^{3}+2^{6}q^{4}+(62+\cdots)q^{5}+\cdots\)
|
38.8.a.e |
\(4\) |
\(11.871\) |
\(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
None |
\(32\) |
\(12\) |
\(-279\) |
\(2485\) |
\(+\) |
\(q+8q^{2}+(3-\beta _{1})q^{3}+2^{6}q^{4}+(-70+\cdots)q^{5}+\cdots\)
|
38.8.c.a |
\(12\) |
\(11.871\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
\(-48\) |
\(12\) |
\(124\) |
\(-1036\) |
|
\(q+8\beta _{2}q^{2}+(\beta _{1}-2\beta _{2})q^{3}+(-2^{6}-2^{6}\beta _{2}+\cdots)q^{4}+\cdots\)
|
38.8.c.b |
\(14\) |
\(11.871\) |
\(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
None |
\(56\) |
\(55\) |
\(-126\) |
\(1928\) |
|
\(q+8\beta _{3}q^{2}+(\beta _{1}+\beta _{2}+8\beta _{3})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots\)
|
38.8.e.a |
\(30\) |
\(11.871\) |
|
None |
\(0\) |
\(45\) |
\(0\) |
\(1806\) |
|
|
38.8.e.b |
\(36\) |
\(11.871\) |
|
None |
\(0\) |
\(-84\) |
\(0\) |
\(-2988\) |
|
|
38.9.b.a |
\(12\) |
\(15.480\) |
\(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(558\) |
\(-5422\) |
|
\(q+\beta _{7}q^{2}+(\beta _{6}-\beta _{7})q^{3}-2^{7}q^{4}+(47+\cdots)q^{5}+\cdots\)
|
38.9.d.a |
\(24\) |
\(15.480\) |
|
None |
\(0\) |
\(168\) |
\(-558\) |
\(11992\) |
|
|
38.9.f.a |
\(84\) |
\(15.480\) |
|
None |
\(0\) |
\(-168\) |
\(0\) |
\(-6570\) |
|
|
38.10.a.a |
\(1\) |
\(19.571\) |
\(\Q\) |
None |
\(16\) |
\(-119\) |
\(-684\) |
\(9149\) |
\(+\) |
\(q+2^{4}q^{2}-119q^{3}+2^{8}q^{4}-684q^{5}+\cdots\)
|
38.10.a.b |
\(1\) |
\(19.571\) |
\(\Q\) |
None |
\(16\) |
\(102\) |
\(-1581\) |
\(-4865\) |
\(+\) |
\(q+2^{4}q^{2}+102q^{3}+2^{8}q^{4}-1581q^{5}+\cdots\)
|
38.10.a.c |
\(3\) |
\(19.571\) |
\(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
None |
\(-48\) |
\(3\) |
\(486\) |
\(-13317\) |
\(+\) |
\(q-2^{4}q^{2}+(1+\beta _{1})q^{3}+2^{8}q^{4}+(162+\cdots)q^{5}+\cdots\)
|
38.10.a.d |
\(4\) |
\(19.571\) |
\(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
None |
\(-64\) |
\(84\) |
\(-1395\) |
\(12307\) |
\(-\) |
\(q-2^{4}q^{2}+(21+\beta _{1})q^{3}+2^{8}q^{4}+(-350+\cdots)q^{5}+\cdots\)
|
38.10.a.e |
\(4\) |
\(19.571\) |
\(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
None |
\(64\) |
\(226\) |
\(866\) |
\(2670\) |
\(-\) |
\(q+2^{4}q^{2}+(57+\beta _{2})q^{3}+2^{8}q^{4}+(218+\cdots)q^{5}+\cdots\)
|
38.10.c.a |
\(14\) |
\(19.571\) |
\(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
None |
\(112\) |
\(165\) |
\(909\) |
\(3692\) |
|
\(q+(2^{4}-2^{4}\beta _{2})q^{2}+(24-\beta _{1}-24\beta _{2}+\cdots)q^{3}+\cdots\)
|
38.10.c.b |
\(16\) |
\(19.571\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(-128\) |
\(70\) |
\(-341\) |
\(3704\) |
|
\(q+(-2^{4}+2^{4}\beta _{2})q^{2}+(9-\beta _{1}-9\beta _{2}+\cdots)q^{3}+\cdots\)
|
38.10.e.a |
\(42\) |
\(19.571\) |
|
None |
\(0\) |
\(-252\) |
\(0\) |
\(14373\) |
|
|