12.3.c.a |
\(1\) |
\(0.327\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(-3\) |
\(0\) |
\(2\) |
|
\(q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots\)
|
12.3.d.a |
\(2\) |
\(0.327\) |
\(\Q(\sqrt{-3}) \) |
None |
\(-2\) |
\(0\) |
\(-4\) |
\(0\) |
|
\(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
|
12.4.a.a |
\(1\) |
\(0.708\) |
\(\Q\) |
None |
\(0\) |
\(3\) |
\(-18\) |
\(8\) |
\(+\) |
\(q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
|
12.4.b.a |
\(4\) |
\(0.708\) |
\(\Q(\sqrt{3}, \sqrt{-5})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
|
12.5.c.a |
\(1\) |
\(1.240\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(9\) |
\(0\) |
\(-94\) |
|
\(q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\)
|
12.5.d.a |
\(4\) |
\(1.240\) |
\(\Q(\sqrt{-3}, \sqrt{13})\) |
None |
\(6\) |
\(0\) |
\(24\) |
\(0\) |
|
\(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots\)
|
12.6.b.a |
\(8\) |
\(1.925\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(1-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
|
12.7.c.a |
\(2\) |
\(2.761\) |
\(\Q(\sqrt{-5}) \) |
None |
\(0\) |
\(-6\) |
\(0\) |
\(484\) |
|
\(q+(-3+\beta )q^{3}+6\beta q^{5}+242q^{7}+(-711+\cdots)q^{9}+\cdots\)
|
12.7.d.a |
\(6\) |
\(2.761\) |
6.0.50898483.1 |
None |
\(-10\) |
\(0\) |
\(-44\) |
\(0\) |
|
\(q+(-2-\beta _{1})q^{2}-\beta _{2}q^{3}+(3^{3}+2\beta _{1}+\cdots)q^{4}+\cdots\)
|
12.8.a.a |
\(1\) |
\(3.749\) |
\(\Q\) |
None |
\(0\) |
\(-27\) |
\(-378\) |
\(-832\) |
\(-\) |
\(q-3^{3}q^{3}-378q^{5}-832q^{7}+3^{6}q^{9}+\cdots\)
|
12.8.a.b |
\(1\) |
\(3.749\) |
\(\Q\) |
None |
\(0\) |
\(27\) |
\(270\) |
\(1112\) |
\(+\) |
\(q+3^{3}q^{3}+270q^{5}+1112q^{7}+3^{6}q^{9}+\cdots\)
|
12.8.b.a |
\(4\) |
\(3.749\) |
\(\Q(\sqrt{3}, \sqrt{-5})\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{3}q^{2}+(-3\beta _{2}+3\beta _{3})q^{3}+(88+4\beta _{1}+\cdots)q^{4}+\cdots\)
|
12.8.b.b |
\(8\) |
\(3.749\) |
\(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-41+\beta _{2}+\cdots)q^{4}+\cdots\)
|
12.9.c.a |
\(1\) |
\(4.889\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(81\) |
\(0\) |
\(4034\) |
|
\(q+3^{4}q^{3}+4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots\)
|
12.9.c.b |
\(2\) |
\(4.889\) |
\(\Q(\sqrt{-110}) \) |
None |
\(0\) |
\(-102\) |
\(0\) |
\(-6188\) |
|
\(q+(-51+\beta )q^{3}-18\beta q^{5}-3094q^{7}+\cdots\)
|
12.9.d.a |
\(8\) |
\(4.889\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(6\) |
\(0\) |
\(-336\) |
\(0\) |
|
\(q+(1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots\)
|
12.10.a.a |
\(1\) |
\(6.180\) |
\(\Q\) |
None |
\(0\) |
\(-81\) |
\(990\) |
\(8576\) |
\(-\) |
\(q-3^{4}q^{3}+990q^{5}+8576q^{7}+3^{8}q^{9}+\cdots\)
|
12.10.b.a |
\(16\) |
\(6.180\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q-\beta _{2}q^{2}-\beta _{4}q^{3}+(-21-\beta _{1})q^{4}+\cdots\)
|
12.11.c.a |
\(1\) |
\(7.624\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(-243\) |
\(0\) |
\(22082\) |
|
\(q-3^{5}q^{3}+22082q^{7}+3^{10}q^{9}+702218q^{13}+\cdots\)
|
12.11.c.b |
\(2\) |
\(7.624\) |
\(\Q(\sqrt{-35}) \) |
None |
\(0\) |
\(234\) |
\(0\) |
\(-20636\) |
|
\(q+(117+\beta )q^{3}+6\beta q^{5}-10318q^{7}+\cdots\)
|
12.11.d.a |
\(10\) |
\(7.624\) |
\(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
None |
\(22\) |
\(0\) |
\(3116\) |
\(0\) |
|
\(q+(2-\beta _{2})q^{2}+\beta _{1}q^{3}+(-65-2\beta _{1}+\cdots)q^{4}+\cdots\)
|
12.12.a.a |
\(1\) |
\(9.220\) |
\(\Q\) |
None |
\(0\) |
\(-243\) |
\(9990\) |
\(-86128\) |
\(-\) |
\(q-3^{5}q^{3}+9990q^{5}-86128q^{7}+3^{10}q^{9}+\cdots\)
|
12.12.a.b |
\(1\) |
\(9.220\) |
\(\Q\) |
None |
\(0\) |
\(243\) |
\(2862\) |
\(9128\) |
\(+\) |
\(q+3^{5}q^{3}+2862q^{5}+9128q^{7}+3^{10}q^{9}+\cdots\)
|
12.12.b.a |
\(20\) |
\(9.220\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(99+\beta _{2})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots\)
|
12.13.c.a |
\(4\) |
\(10.968\) |
\(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
None |
\(0\) |
\(300\) |
\(0\) |
\(15800\) |
|
\(q+(75+\beta _{1})q^{3}+(-3\beta _{1}+\beta _{2})q^{5}+(3950+\cdots)q^{7}+\cdots\)
|
12.13.d.a |
\(12\) |
\(10.968\) |
\(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
None |
\(-90\) |
\(0\) |
\(-10296\) |
\(0\) |
|
\(q+(-8+\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-386+\cdots)q^{4}+\cdots\)
|
12.14.a.a |
\(1\) |
\(12.868\) |
\(\Q\) |
None |
\(0\) |
\(-729\) |
\(-14850\) |
\(-62896\) |
\(-\) |
\(q-3^{6}q^{3}-14850q^{5}-62896q^{7}+\cdots\)
|
12.14.a.b |
\(1\) |
\(12.868\) |
\(\Q\) |
None |
\(0\) |
\(729\) |
\(-24570\) |
\(-173704\) |
\(+\) |
\(q+3^{6}q^{3}-24570q^{5}-173704q^{7}+\cdots\)
|
12.14.b.a |
\(24\) |
\(12.868\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
12.15.c.a |
\(1\) |
\(14.919\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(-2187\) |
\(0\) |
\(-1389022\) |
|
\(q-3^{7}q^{3}-1389022q^{7}+3^{14}q^{9}+\cdots\)
|
12.15.c.b |
\(4\) |
\(14.919\) |
\(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
None |
\(0\) |
\(2148\) |
\(0\) |
\(1709288\) |
|
\(q+(537-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(427322+\cdots)q^{7}+\cdots\)
|
12.15.d.a |
\(14\) |
\(14.919\) |
\(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
None |
\(182\) |
\(0\) |
\(-16124\) |
\(0\) |
|
\(q+(13-\beta _{1})q^{2}+\beta _{2}q^{3}+(665-13\beta _{1}+\cdots)q^{4}+\cdots\)
|
12.16.a.a |
\(1\) |
\(17.123\) |
\(\Q\) |
None |
\(0\) |
\(-2187\) |
\(45702\) |
\(1217888\) |
\(-\) |
\(q-3^{7}q^{3}+45702q^{5}+1217888q^{7}+\cdots\)
|
12.16.a.b |
\(2\) |
\(17.123\) |
\(\Q(\sqrt{8017}) \) |
None |
\(0\) |
\(4374\) |
\(69660\) |
\(2491504\) |
\(+\) |
\(q+3^{7}q^{3}+(34830-\beta )q^{5}+(1245752+\cdots)q^{7}+\cdots\)
|
12.16.b.a |
\(28\) |
\(17.123\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
12.17.c.a |
\(1\) |
\(19.479\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(6561\) |
\(0\) |
\(4743554\) |
|
\(q+3^{8}q^{3}+4743554q^{7}+3^{16}q^{9}+\cdots\)
|
12.17.c.b |
\(4\) |
\(19.479\) |
\(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
None |
\(0\) |
\(-12420\) |
\(0\) |
\(-1050280\) |
|
\(q+(-3105-\beta _{1})q^{3}+(-8\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
|
12.17.d.a |
\(16\) |
\(19.479\) |
\(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
None |
\(-186\) |
\(0\) |
\(354144\) |
\(0\) |
|
\(q+(-12-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(8542+\cdots)q^{4}+\cdots\)
|
12.18.a.a |
\(1\) |
\(21.987\) |
\(\Q\) |
None |
\(0\) |
\(-6561\) |
\(-1608930\) |
\(-9417184\) |
\(-\) |
\(q-3^{8}q^{3}-1608930q^{5}-9417184q^{7}+\cdots\)
|
12.18.a.b |
\(1\) |
\(21.987\) |
\(\Q\) |
None |
\(0\) |
\(6561\) |
\(130950\) |
\(-14846776\) |
\(+\) |
\(q+3^{8}q^{3}+130950q^{5}-14846776q^{7}+\cdots\)
|
12.18.b.a |
\(32\) |
\(21.987\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
12.19.c.a |
\(6\) |
\(24.646\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(0\) |
\(23934\) |
\(0\) |
\(11024364\) |
|
\(q+(3989-\beta _{1})q^{3}+(-4\beta _{1}+\beta _{2})q^{5}+\cdots\)
|
12.19.d.a |
\(18\) |
\(24.646\) |
\(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
None |
\(-170\) |
\(0\) |
\(-1721764\) |
\(0\) |
|
\(q+(-9-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-24281+\cdots)q^{4}+\cdots\)
|
12.20.a.a |
\(2\) |
\(27.458\) |
\(\Q(\sqrt{193153}) \) |
None |
\(0\) |
\(-39366\) |
\(624780\) |
\(4667104\) |
\(-\) |
\(q-3^{9}q^{3}+(312390-\beta )q^{5}+(2333552+\cdots)q^{7}+\cdots\)
|
12.20.a.b |
\(2\) |
\(27.458\) |
\(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
None |
\(0\) |
\(39366\) |
\(-3267108\) |
\(-27023984\) |
\(+\) |
\(q+3^{9}q^{3}+(-1633554-\beta )q^{5}+(-13511992+\cdots)q^{7}+\cdots\)
|
12.20.b.a |
\(36\) |
\(27.458\) |
|
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
|
|
12.21.c.a |
\(1\) |
\(30.422\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(59049\) |
\(0\) |
\(-77335774\) |
|
\(q+3^{10}q^{3}-77335774q^{7}+3^{20}q^{9}+\cdots\)
|
12.21.c.b |
\(6\) |
\(30.422\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(0\) |
\(-84378\) |
\(0\) |
\(-145040532\) |
|
\(q+(-14063+\beta _{1})q^{3}+(3^{3}\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
|
12.21.d.a |
\(20\) |
\(30.422\) |
\(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
None |
\(1254\) |
\(0\) |
\(1476984\) |
\(0\) |
|
\(q+(63-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
|
12.22.a.a |
\(1\) |
\(33.537\) |
\(\Q\) |
None |
\(0\) |
\(59049\) |
\(-11268090\) |
\(281914136\) |
\(+\) |
\(q+3^{10}q^{3}-11268090q^{5}+281914136q^{7}+\cdots\)
|