1001.1.r.a |
\(4\) |
\(0.500\) |
\(\Q(\zeta_{12})\) |
\(A_{4}\)
|
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
\(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
|
1001.1.y.a |
\(2\) |
\(0.500\) |
\(\Q(\sqrt{-3}) \) |
\(D_{3}\)
|
\(\Q(\sqrt{-143}) \) |
None |
\(-1\) |
\(1\) |
\(0\) |
\(1\) |
\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots\)
|
1001.1.y.b |
\(2\) |
\(0.500\) |
\(\Q(\sqrt{-3}) \) |
\(D_{3}\)
|
\(\Q(\sqrt{-143}) \) |
None |
\(1\) |
\(1\) |
\(0\) |
\(-1\) |
\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots\)
|
1001.1.y.c |
\(8\) |
\(0.500\) |
\(\Q(\zeta_{15})\) |
\(D_{15}\)
|
\(\Q(\sqrt{-143}) \) |
None |
\(-1\) |
\(-1\) |
\(0\) |
\(1\) |
\(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
|
1001.1.y.d |
\(8\) |
\(0.500\) |
\(\Q(\zeta_{15})\) |
\(D_{15}\)
|
\(\Q(\sqrt{-143}) \) |
None |
\(1\) |
\(-1\) |
\(0\) |
\(-1\) |
\(q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
|
1001.1.bo.a |
\(4\) |
\(0.500\) |
\(\Q(\zeta_{12})\) |
\(A_{4}\)
|
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
\(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
|
1003.1.b.a |
\(1\) |
\(0.501\) |
\(\Q\) |
\(D_{2}\)
|
\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1003}) \) |
\(\Q(\sqrt{17}) \) |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots\)
|
1003.1.b.b |
\(2\) |
\(0.501\) |
\(\Q(\sqrt{-3}) \) |
\(D_{6}\)
|
\(\Q(\sqrt{-59}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
|
1003.1.f.a |
\(2\) |
\(0.501\) |
\(\Q(\sqrt{-1}) \) |
\(D_{4}\)
|
\(\Q(\sqrt{-59}) \) |
None |
\(0\) |
\(-2\) |
\(-2\) |
\(-2\) |
\(q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots\)
|
1003.1.f.b |
\(4\) |
\(0.501\) |
\(\Q(\zeta_{12})\) |
\(D_{12}\)
|
\(\Q(\sqrt{-59}) \) |
None |
\(0\) |
\(2\) |
\(2\) |
\(2\) |
\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
|
1003.1.h.a |
\(4\) |
\(0.501\) |
\(\Q(\zeta_{8})\) |
\(D_{8}\)
|
\(\Q(\sqrt{-59}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
|
1003.1.h.b |
\(8\) |
\(0.501\) |
\(\Q(\zeta_{24})\) |
\(D_{24}\)
|
\(\Q(\sqrt{-59}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
|
1004.1.d.a |
\(1\) |
\(0.501\) |
\(\Q\) |
\(D_{3}\)
|
\(\Q(\sqrt{-251}) \) |
None |
\(0\) |
\(2\) |
\(-1\) |
\(-1\) |
\(q+2q^{3}-q^{5}-q^{7}+3q^{9}+2q^{13}+\cdots\)
|
1004.1.d.b |
\(6\) |
\(0.501\) |
\(\Q(\zeta_{21})^+\) |
\(D_{21}\)
|
\(\Q(\sqrt{-251}) \) |
None |
\(0\) |
\(-2\) |
\(1\) |
\(1\) |
\(q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
|
1005.1.p.a |
\(4\) |
\(0.502\) |
\(\Q(\zeta_{12})\) |
\(A_{4}\)
|
None |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
\(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{3}q^{5}+\cdots\)
|
1005.1.p.b |
\(4\) |
\(0.502\) |
\(\Q(\zeta_{12})\) |
\(A_{4}\)
|
None |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
\(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)
|
1007.1.d.a |
\(1\) |
\(0.503\) |
\(\Q\) |
\(D_{3}\)
|
\(\Q(\sqrt{-1007}) \) |
None |
\(-1\) |
\(-1\) |
\(0\) |
\(2\) |
\(q-q^{2}-q^{3}+q^{6}+2q^{7}+q^{8}-q^{11}+\cdots\)
|
1007.1.d.b |
\(1\) |
\(0.503\) |
\(\Q\) |
\(D_{3}\)
|
\(\Q(\sqrt{-1007}) \) |
None |
\(1\) |
\(1\) |
\(0\) |
\(2\) |
\(q+q^{2}+q^{3}+q^{6}+2q^{7}-q^{8}-q^{11}+\cdots\)
|
1007.1.d.c |
\(2\) |
\(0.503\) |
\(\Q(\sqrt{5}) \) |
\(D_{5}\)
|
\(\Q(\sqrt{-1007}) \) |
None |
\(-1\) |
\(-1\) |
\(0\) |
\(-1\) |
\(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
|
1007.1.d.d |
\(2\) |
\(0.503\) |
\(\Q(\sqrt{5}) \) |
\(D_{5}\)
|
\(\Q(\sqrt{-1007}) \) |
None |
\(1\) |
\(1\) |
\(0\) |
\(-1\) |
\(q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
|
1007.1.d.e |
\(4\) |
\(0.503\) |
\(\Q(\zeta_{15})^+\) |
\(D_{15}\)
|
\(\Q(\sqrt{-1007}) \) |
None |
\(-1\) |
\(-1\) |
\(0\) |
\(-2\) |
\(q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
|
1007.1.d.f |
\(4\) |
\(0.503\) |
\(\Q(\zeta_{15})^+\) |
\(D_{15}\)
|
\(\Q(\sqrt{-1007}) \) |
None |
\(1\) |
\(1\) |
\(0\) |
\(-2\) |
\(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
|
1008.1.f.a |
\(1\) |
\(0.503\) |
\(\Q\) |
\(D_{2}\)
|
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) |
\(\Q(\sqrt{21}) \) |
\(0\) |
\(0\) |
\(0\) |
\(1\) |
\(q+q^{7}+q^{25}-2q^{37}+2q^{43}+q^{49}+\cdots\)
|
1008.1.u.a |
\(2\) |
\(0.503\) |
\(\Q(\sqrt{-1}) \) |
\(D_{4}\)
|
\(\Q(\sqrt{-7}) \) |
None |
\(-2\) |
\(0\) |
\(0\) |
\(0\) |
\(q-q^{2}+q^{4}+iq^{7}-q^{8}+(1-i)q^{11}+\cdots\)
|
1008.1.u.b |
\(2\) |
\(0.503\) |
\(\Q(\sqrt{-1}) \) |
\(D_{4}\)
|
\(\Q(\sqrt{-7}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+(1-i+\cdots)q^{11}+\cdots\)
|
1008.1.u.c |
\(2\) |
\(0.503\) |
\(\Q(\sqrt{-1}) \) |
\(D_{4}\)
|
\(\Q(\sqrt{-7}) \) |
None |
\(2\) |
\(0\) |
\(0\) |
\(0\) |
\(q+q^{2}+q^{4}+iq^{7}+q^{8}+(-1+i+\cdots)q^{11}+\cdots\)
|
1008.1.y.a |
\(4\) |
\(0.503\) |
\(\Q(\zeta_{8})\) |
\(D_{4}\)
|
\(\Q(\sqrt{-7}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
|
1008.1.y.b |
\(4\) |
\(0.503\) |
\(\Q(\zeta_{8})\) |
\(D_{4}\)
|
\(\Q(\sqrt{-7}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(4\) |
\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{7}-\zeta_{8}q^{8}+\cdots\)
|
1008.1.bw.a |
\(4\) |
\(0.503\) |
\(\Q(\zeta_{12})\) |
\(A_{4}\)
|
None |
None |
\(0\) |
\(0\) |
\(2\) |
\(0\) |
\(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
|
1008.1.cd.a |
\(2\) |
\(0.503\) |
\(\Q(\sqrt{-3}) \) |
\(D_{6}\)
|
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
\(q+\zeta_{6}^{2}q^{7}+q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots\)
|
1008.1.cd.b |
\(2\) |
\(0.503\) |
\(\Q(\sqrt{-3}) \) |
\(D_{6}\)
|
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(1\) |
\(q-\zeta_{6}^{2}q^{7}+q^{13}+(-1-\zeta_{6})q^{19}+\cdots\)
|
1008.1.cg.a |
\(2\) |
\(0.503\) |
\(\Q(\sqrt{-3}) \) |
\(D_{6}\)
|
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-1\) |
\(q-\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
|
1008.1.dc.a |
\(4\) |
\(0.503\) |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
\(S_{4}\)
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-2\) |
\(q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)
|
1008.1.dd.a |
\(4\) |
\(0.503\) |
\(\Q(\zeta_{12})\) |
\(A_{4}\)
|
None |
None |
\(0\) |
\(0\) |
\(-4\) |
\(0\) |
\(q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots\)
|
1008.1.dt.a |
\(8\) |
\(0.503\) |
\(\Q(\zeta_{24})\) |
\(S_{4}\)
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
\(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots\)
|
1008.1.ed.a |
\(8\) |
\(0.503\) |
\(\Q(\zeta_{24})\) |
\(S_{4}\)
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}q^{5}+\zeta_{24}^{2}q^{7}+\cdots\)
|
1011.1.c.a |
\(1\) |
\(0.505\) |
\(\Q\) |
\(D_{2}\)
|
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1011}) \) |
\(\Q(\sqrt{337}) \) |
\(0\) |
\(-1\) |
\(0\) |
\(2\) |
\(q-q^{3}+q^{4}+2q^{7}+q^{9}-q^{12}-2q^{13}+\cdots\)
|
1011.1.c.b |
\(1\) |
\(0.505\) |
\(\Q\) |
\(D_{3}\)
|
\(\Q(\sqrt{-1011}) \) |
None |
\(0\) |
\(1\) |
\(-1\) |
\(-1\) |
\(q+q^{3}+q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
|
1011.1.c.c |
\(1\) |
\(0.505\) |
\(\Q\) |
\(D_{3}\)
|
\(\Q(\sqrt{-1011}) \) |
None |
\(0\) |
\(1\) |
\(1\) |
\(-1\) |
\(q+q^{3}+q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
|
1011.1.c.d |
\(2\) |
\(0.505\) |
\(\Q(\sqrt{3}) \) |
\(D_{6}\)
|
\(\Q(\sqrt{-1011}) \) |
None |
\(0\) |
\(-2\) |
\(0\) |
\(-2\) |
\(q-q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}-q^{12}+\cdots\)
|
1011.1.f.a |
\(2\) |
\(0.505\) |
\(\Q(\sqrt{-1}) \) |
\(D_{4}\)
|
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q-iq^{3}+q^{4}-q^{9}-iq^{12}+q^{16}+\cdots\)
|
1011.1.f.b |
\(4\) |
\(0.505\) |
\(\Q(\zeta_{8})\) |
\(S_{4}\)
|
None |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)
|
1011.1.l.a |
\(4\) |
\(0.505\) |
\(\Q(\zeta_{8})\) |
\(D_{8}\)
|
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(-4\) |
\(q-\zeta_{8}^{3}q^{3}+q^{4}+(-1-\zeta_{8}^{2})q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
|
1011.1.q.a |
\(6\) |
\(0.505\) |
\(\Q(\zeta_{14})\) |
\(D_{14}\)
|
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(1\) |
\(0\) |
\(-2\) |
\(q-\zeta_{14}^{6}q^{3}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}-\zeta_{14}^{5}+\cdots)q^{7}+\cdots\)
|
1011.1.r.a |
\(6\) |
\(0.505\) |
\(\Q(\zeta_{14})\) |
\(D_{7}\)
|
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(-1\) |
\(0\) |
\(-2\) |
\(q-\zeta_{14}^{3}q^{3}-\zeta_{14}^{3}q^{4}+(\zeta_{14}^{4}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\)
|
1011.1.y.a |
\(12\) |
\(0.505\) |
\(\Q(\zeta_{28})\) |
\(D_{28}\)
|
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
\(q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}^{4}+\cdots)q^{7}+\cdots\)
|
1011.1.bf.a |
\(24\) |
\(0.505\) |
\(\Q(\zeta_{56})\) |
\(D_{56}\)
|
\(\Q(\sqrt{-3}) \) |
None |
\(0\) |
\(0\) |
\(0\) |
\(4\) |
\(q-\zeta_{56}^{15}q^{3}+\zeta_{56}^{8}q^{4}+(\zeta_{56}^{6}-\zeta_{56}^{16}+\cdots)q^{7}+\cdots\)
|
1012.1.r.a |
\(20\) |
\(0.505\) |
\(\Q(\zeta_{33})\) |
\(D_{33}\)
|
\(\Q(\sqrt{-11}) \) |
None |
\(0\) |
\(2\) |
\(2\) |
\(0\) |
\(q+(\zeta_{66}^{2}-\zeta_{66}^{19})q^{3}+(-\zeta_{66}^{25}+\zeta_{66}^{32}+\cdots)q^{5}+\cdots\)
|
1015.1.f.a |
\(1\) |
\(0.507\) |
\(\Q\) |
\(D_{2}\)
|
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \) |
\(\Q(\sqrt{29}) \) |
\(0\) |
\(0\) |
\(-1\) |
\(-1\) |
\(q-q^{4}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{16}+\cdots\)
|
1015.1.f.b |
\(1\) |
\(0.507\) |
\(\Q\) |
\(D_{2}\)
|
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-1015}) \) |
\(\Q(\sqrt{29}) \) |
\(0\) |
\(0\) |
\(1\) |
\(1\) |
\(q-q^{4}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{16}+\cdots\)
|