1.18.a.a |
\(1\) |
\(1.832\) |
\(\Q\) |
None |
\(-528\) |
\(-4284\) |
\(-1025850\) |
\(3225992\) |
\(+\) |
\(q-528q^{2}-4284q^{3}+147712q^{4}+\cdots\)
|
1.20.a.a |
\(1\) |
\(2.288\) |
\(\Q\) |
None |
\(456\) |
\(50652\) |
\(-2377410\) |
\(-16917544\) |
\(+\) |
\(q+456q^{2}+50652q^{3}-316352q^{4}+\cdots\)
|
1.22.a.a |
\(1\) |
\(2.795\) |
\(\Q\) |
None |
\(-288\) |
\(-128844\) |
\(21640950\) |
\(-768078808\) |
\(+\) |
\(q-288q^{2}-128844q^{3}-2014208q^{4}+\cdots\)
|
1.24.a.a |
\(2\) |
\(3.352\) |
\(\Q(\sqrt{144169}) \) |
None |
\(1080\) |
\(339480\) |
\(73069020\) |
\(-1359184400\) |
\(+\) |
\(q+(540-\beta )q^{2}+(169740+48\beta )q^{3}+\cdots\)
|
2.18.a.a |
\(1\) |
\(3.664\) |
\(\Q\) |
None |
\(256\) |
\(6084\) |
\(1255110\) |
\(-22465912\) |
\(-\) |
\(q+2^{8}q^{2}+78^{2}q^{3}+2^{16}q^{4}+1255110q^{5}+\cdots\)
|
1.26.a.a |
\(1\) |
\(3.960\) |
\(\Q\) |
None |
\(-48\) |
\(-195804\) |
\(-741989850\) |
\(39080597192\) |
\(+\) |
\(q-48q^{2}-195804q^{3}-33552128q^{4}+\cdots\)
|
2.20.a.a |
\(1\) |
\(4.576\) |
\(\Q\) |
None |
\(-512\) |
\(-13092\) |
\(6546750\) |
\(96674264\) |
\(+\) |
\(q-2^{9}q^{2}-13092q^{3}+2^{18}q^{4}+6546750q^{5}+\cdots\)
|
2.20.a.b |
\(1\) |
\(4.576\) |
\(\Q\) |
None |
\(512\) |
\(-53028\) |
\(-5556930\) |
\(-44496424\) |
\(-\) |
\(q+2^{9}q^{2}-53028q^{3}+2^{18}q^{4}-5556930q^{5}+\cdots\)
|
1.28.a.a |
\(2\) |
\(4.619\) |
\(\Q(\sqrt{18209}) \) |
None |
\(-8280\) |
\(-1286280\) |
\(5443587900\) |
\(-175391963600\) |
\(+\) |
\(q+(-4140-\beta )q^{2}+(-643140-192\beta )q^{3}+\cdots\)
|
3.17.b.a |
\(4\) |
\(4.870\) |
\(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
None |
\(0\) |
\(-2052\) |
\(0\) |
\(-3141544\) |
|
\(q+\beta _{1}q^{2}+(-513+\beta _{1}+\beta _{2})q^{3}+(-3116+\cdots)q^{4}+\cdots\)
|
1.30.a.a |
\(2\) |
\(5.328\) |
\(\Q(\sqrt{51349}) \) |
None |
\(8640\) |
\(-4967640\) |
\(-17477788500\) |
\(-3\!\cdots\!00\) |
\(+\) |
\(q+(4320-\beta )q^{2}+(-2483820+552\beta )q^{3}+\cdots\)
|
3.18.a.a |
\(1\) |
\(5.497\) |
\(\Q\) |
None |
\(204\) |
\(-6561\) |
\(-163554\) |
\(-20846560\) |
\(+\) |
\(q+204q^{2}-3^{8}q^{3}-89456q^{4}-163554q^{5}+\cdots\)
|
3.18.a.b |
\(2\) |
\(5.497\) |
\(\Q(\sqrt{14569}) \) |
None |
\(594\) |
\(13122\) |
\(382860\) |
\(24471568\) |
\(-\) |
\(q+(297-\beta )q^{2}+3^{8}q^{3}+(88258-594\beta )q^{4}+\cdots\)
|
2.22.a.a |
\(1\) |
\(5.590\) |
\(\Q\) |
None |
\(-1024\) |
\(71604\) |
\(-28693770\) |
\(-853202392\) |
\(+\) |
\(q-2^{10}q^{2}+71604q^{3}+2^{20}q^{4}-28693770q^{5}+\cdots\)
|
2.22.a.b |
\(1\) |
\(5.590\) |
\(\Q\) |
None |
\(1024\) |
\(59316\) |
\(4975350\) |
\(1427425832\) |
\(-\) |
\(q+2^{10}q^{2}+59316q^{3}+2^{20}q^{4}+4975350q^{5}+\cdots\)
|
1.32.a.a |
\(2\) |
\(6.088\) |
\(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
None |
\(39960\) |
\(17363160\) |
\(-19391218020\) |
\(30\!\cdots\!00\) |
\(+\) |
\(q+(19980-\beta )q^{2}+(8681580-432\beta )q^{3}+\cdots\)
|
3.19.b.a |
\(1\) |
\(6.162\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(-19683\) |
\(0\) |
\(77549186\) |
|
\(q-3^{9}q^{3}+2^{18}q^{4}+77549186q^{7}+\cdots\)
|
3.19.b.b |
\(4\) |
\(6.162\) |
4.0.601940665.1 |
None |
\(0\) |
\(15876\) |
\(0\) |
\(-95744152\) |
|
\(q-\beta _{1}q^{2}+(63^{2}+11\beta _{1}+\beta _{2})q^{3}+(-263384+\cdots)q^{4}+\cdots\)
|
4.17.b.a |
\(1\) |
\(6.493\) |
\(\Q\) |
\(\Q(\sqrt{-1}) \) |
\(256\) |
\(0\) |
\(329666\) |
\(0\) |
|
\(q+2^{8}q^{2}+2^{16}q^{4}+329666q^{5}+2^{24}q^{8}+\cdots\)
|
4.17.b.b |
\(6\) |
\(6.493\) |
\(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
None |
\(-164\) |
\(0\) |
\(-506740\) |
\(0\) |
|
\(q+(-3^{3}-\beta _{1})q^{2}+(1-3\beta _{1}+\beta _{2})q^{3}+\cdots\)
|
2.24.a.a |
\(1\) |
\(6.704\) |
\(\Q\) |
None |
\(-2048\) |
\(-505908\) |
\(-90135570\) |
\(6872255096\) |
\(+\) |
\(q-2^{11}q^{2}-505908q^{3}+2^{22}q^{4}+\cdots\)
|
3.20.a.a |
\(1\) |
\(6.865\) |
\(\Q\) |
None |
\(-1104\) |
\(19683\) |
\(3516270\) |
\(-195590584\) |
\(-\) |
\(q-1104q^{2}+3^{9}q^{3}+694528q^{4}+\cdots\)
|
3.20.a.b |
\(2\) |
\(6.865\) |
\(\Q(\sqrt{87481}) \) |
None |
\(702\) |
\(-39366\) |
\(6016140\) |
\(113892064\) |
\(+\) |
\(q+(351-\beta )q^{2}-3^{9}q^{3}+(386242-702\beta )q^{4}+\cdots\)
|
4.18.a.a |
\(2\) |
\(7.329\) |
\(\Q(\sqrt{9361}) \) |
None |
\(0\) |
\(-5880\) |
\(604044\) |
\(25350160\) |
\(-\) |
\(q+(-2940-\beta )q^{3}+(302022+6^{2}\beta )q^{5}+\cdots\)
|
3.21.b.a |
\(6\) |
\(7.605\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(0\) |
\(-4122\) |
\(0\) |
\(559607916\) |
|
\(q+\beta _{1}q^{2}+(-687+11\beta _{1}+\beta _{2})q^{3}+\cdots\)
|
2.26.a.a |
\(1\) |
\(7.920\) |
\(\Q\) |
None |
\(-4096\) |
\(97956\) |
\(341005350\) |
\(-40882637368\) |
\(+\) |
\(q-2^{12}q^{2}+97956q^{3}+2^{24}q^{4}+341005350q^{5}+\cdots\)
|
2.26.a.b |
\(2\) |
\(7.920\) |
\(\Q(\sqrt{106705}) \) |
None |
\(8192\) |
\(379848\) |
\(741953100\) |
\(-376536944\) |
\(-\) |
\(q+2^{12}q^{2}+(189924-\beta )q^{3}+2^{24}q^{4}+\cdots\)
|
5.17.c.a |
\(14\) |
\(8.116\) |
\(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
None |
\(-2\) |
\(7908\) |
\(192880\) |
\(-386452\) |
|
\(q-\beta _{2}q^{2}+(565-3\beta _{1}-565\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
|
4.19.b.a |
\(8\) |
\(8.215\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(84\) |
\(0\) |
\(860880\) |
\(0\) |
|
\(q+(11-\beta _{1})q^{2}-\beta _{2}q^{3}+(44007-9\beta _{1}+\cdots)q^{4}+\cdots\)
|
3.22.a.a |
\(1\) |
\(8.384\) |
\(\Q\) |
None |
\(-2844\) |
\(-59049\) |
\(3109950\) |
\(363303920\) |
\(+\) |
\(q-2844q^{2}-3^{10}q^{3}+5991184q^{4}+\cdots\)
|
3.22.a.b |
\(1\) |
\(8.384\) |
\(\Q\) |
None |
\(1728\) |
\(-59049\) |
\(-41512770\) |
\(538429808\) |
\(+\) |
\(q+12^{3}q^{2}-3^{10}q^{3}+888832q^{4}+\cdots\)
|
3.22.a.c |
\(2\) |
\(8.384\) |
\(\Q(\sqrt{649}) \) |
None |
\(666\) |
\(118098\) |
\(996876\) |
\(679896112\) |
\(-\) |
\(q+(333-\beta )q^{2}+3^{10}q^{3}+(589618+\cdots)q^{4}+\cdots\)
|
4.20.a.a |
\(1\) |
\(9.153\) |
\(\Q\) |
None |
\(0\) |
\(-36\) |
\(-196290\) |
\(-35905576\) |
\(-\) |
\(q-6^{2}q^{3}-196290q^{5}-35905576q^{7}+\cdots\)
|
5.18.a.a |
\(2\) |
\(9.161\) |
\(\Q(\sqrt{39}) \) |
None |
\(680\) |
\(-10980\) |
\(-781250\) |
\(-22820700\) |
\(+\) |
\(q+(340+\beta )q^{2}+(-5490-52\beta )q^{3}+\cdots\)
|
5.18.a.b |
\(3\) |
\(9.161\) |
\(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
None |
\(118\) |
\(15944\) |
\(1171875\) |
\(2139308\) |
\(-\) |
\(q+(39-\beta _{1})q^{2}+(5317+8\beta _{1}+\beta _{2})q^{3}+\cdots\)
|
5.18.b.a |
\(8\) |
\(9.161\) |
\(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
None |
\(0\) |
\(0\) |
\(379200\) |
\(0\) |
|
\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-72387+\beta _{3}+\cdots)q^{4}+\cdots\)
|
3.23.b.a |
\(6\) |
\(9.201\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(0\) |
\(86670\) |
\(0\) |
\(-3447063060\) |
|
\(q+\beta _{1}q^{2}+(14445-8\beta _{1}+\beta _{2})q^{3}+\cdots\)
|
2.28.a.a |
\(1\) |
\(9.237\) |
\(\Q\) |
None |
\(-8192\) |
\(3984828\) |
\(-2851889250\) |
\(368721063704\) |
\(+\) |
\(q-2^{13}q^{2}+3984828q^{3}+2^{26}q^{4}+\cdots\)
|
2.28.a.b |
\(1\) |
\(9.237\) |
\(\Q\) |
None |
\(8192\) |
\(-1016388\) |
\(-3341197410\) |
\(-51021361384\) |
\(-\) |
\(q+2^{13}q^{2}-1016388q^{3}+2^{26}q^{4}+\cdots\)
|
6.17.b.a |
\(6\) |
\(9.739\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(0\) |
\(6006\) |
\(0\) |
\(-167892\) |
|
\(q-\beta _{1}q^{2}+(1001+\beta _{1}-\beta _{2})q^{3}-2^{15}q^{4}+\cdots\)
|
3.24.a.a |
\(1\) |
\(10.056\) |
\(\Q\) |
None |
\(1128\) |
\(177147\) |
\(-48863730\) |
\(-1723688680\) |
\(-\) |
\(q+1128q^{2}+3^{11}q^{3}-7116224q^{4}+\cdots\)
|
3.24.a.b |
\(2\) |
\(10.056\) |
\(\Q(\sqrt{530401}) \) |
None |
\(-1242\) |
\(-354294\) |
\(-46808820\) |
\(-211963904\) |
\(+\) |
\(q+(-621-\beta )q^{2}-3^{11}q^{3}+(-3229358+\cdots)q^{4}+\cdots\)
|
4.21.b.a |
\(1\) |
\(10.141\) |
\(\Q\) |
\(\Q(\sqrt{-1}) \) |
\(-1024\) |
\(0\) |
\(-19306574\) |
\(0\) |
|
\(q-2^{10}q^{2}+2^{20}q^{4}-19306574q^{5}+\cdots\)
|
4.21.b.b |
\(8\) |
\(10.141\) |
\(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
None |
\(396\) |
\(0\) |
\(18568080\) |
\(0\) |
|
\(q+(7^{2}+\beta _{1})q^{2}+(6-12\beta _{1}-\beta _{2})q^{3}+\cdots\)
|
5.19.c.a |
\(16\) |
\(10.269\) |
\(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
None |
\(510\) |
\(-20130\) |
\(3145170\) |
\(78767350\) |
|
\(q+(2^{5}+\beta _{2}+2^{5}\beta _{4})q^{2}+(-1259-5\beta _{1}+\cdots)q^{3}+\cdots\)
|
2.30.a.a |
\(1\) |
\(10.656\) |
\(\Q\) |
None |
\(-16384\) |
\(-2792556\) |
\(6651856470\) |
\(14\!\cdots\!48\) |
\(+\) |
\(q-2^{14}q^{2}-2792556q^{3}+2^{28}q^{4}+\cdots\)
|
2.30.a.b |
\(1\) |
\(10.656\) |
\(\Q\) |
None |
\(16384\) |
\(4782996\) |
\(6065841750\) |
\(904018883432\) |
\(-\) |
\(q+2^{14}q^{2}+4782996q^{3}+2^{28}q^{4}+\cdots\)
|
3.25.b.a |
\(1\) |
\(10.949\) |
\(\Q\) |
\(\Q(\sqrt{-3}) \) |
\(0\) |
\(531441\) |
\(0\) |
\(-4119710398\) |
|
\(q+3^{12}q^{3}+2^{24}q^{4}-4119710398q^{7}+\cdots\)
|
3.25.b.b |
\(6\) |
\(10.949\) |
\(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
None |
\(0\) |
\(-616842\) |
\(0\) |
\(1988064876\) |
|
\(q+\beta _{1}q^{2}+(-102807+2^{4}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
|
6.18.a.a |
\(1\) |
\(10.993\) |
\(\Q\) |
None |
\(-256\) |
\(-6561\) |
\(645150\) |
\(3974432\) |
\(+\) |
\(q-2^{8}q^{2}-3^{8}q^{3}+2^{16}q^{4}+645150q^{5}+\cdots\)
|