Label |
Level |
Weight |
Char |
Prim |
Char order |
Dim |
Rel. Dim |
$A$ |
Field |
Image |
CM |
RM |
Self-dual |
Inner twists |
Rank* |
Traces |
Coefficient ring index |
Sato-Tate |
$q$-expansion |
$a_{2}$ |
$a_{3}$ |
$a_{5}$ |
$a_{7}$ |
143.1.d.a |
$143$ |
$1$ |
143.d |
143.d |
$2$ |
$2$ |
$2$ |
$0.071$ |
\(\Q(\sqrt{5}) \) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
✓ |
$2$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\) |
143.1.d.b |
$143$ |
$1$ |
143.d |
143.d |
$2$ |
$2$ |
$2$ |
$0.071$ |
\(\Q(\sqrt{5}) \) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
✓ |
$2$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+(1-\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\) |
1001.1.y.a |
$1001$ |
$1$ |
1001.y |
1001.y |
$6$ |
$2$ |
$1$ |
$0.500$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots\) |
1001.1.y.b |
$1001$ |
$1$ |
1001.y |
1001.y |
$6$ |
$2$ |
$1$ |
$0.500$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots\) |
1001.1.y.c |
$1001$ |
$1$ |
1001.y |
1001.y |
$6$ |
$8$ |
$4$ |
$0.500$ |
\(\Q(\zeta_{15})\) |
$D_{15}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\) |
1001.1.y.d |
$1001$ |
$1$ |
1001.y |
1001.y |
$6$ |
$8$ |
$4$ |
$0.500$ |
\(\Q(\zeta_{15})\) |
$D_{15}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\) |
1144.1.h.e |
$1144$ |
$1$ |
1144.h |
1144.h |
$2$ |
$2$ |
$2$ |
$0.571$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-22}) \), \(\Q(\sqrt{-143}) \) |
\(\Q(\sqrt{26}) \) |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{4}+iq^{8}+q^{9}-iq^{11}+\cdots\) |
1144.1.h.f |
$1144$ |
$1$ |
1144.h |
1144.h |
$2$ |
$8$ |
$8$ |
$0.571$ |
\(\Q(\zeta_{20})\) |
$D_{10}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(0\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{20}q^{2}+(-\zeta_{20}^{4}-\zeta_{20}^{6})q^{3}+\zeta_{20}^{2}q^{4}+\cdots\) |
1287.1.g.a |
$1287$ |
$1$ |
1287.g |
143.d |
$2$ |
$2$ |
$2$ |
$0.642$ |
\(\Q(\sqrt{5}) \) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
✓ |
$2$ |
$0$ |
\(-1\) |
\(0\) |
\(0\) |
\(1\) |
$1$ |
|
\(q-\beta q^{2}+\beta q^{4}+(1-\beta )q^{7}-q^{8}+q^{11}+\cdots\) |
1287.1.g.b |
$1287$ |
$1$ |
1287.g |
143.d |
$2$ |
$2$ |
$2$ |
$0.642$ |
\(\Q(\sqrt{5}) \) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
✓ |
$2$ |
$0$ |
\(1\) |
\(0\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+\beta q^{2}+\beta q^{4}+(-1+\beta )q^{7}+q^{8}+\cdots\) |
1287.1.ba.a |
$1287$ |
$1$ |
1287.ba |
1287.aa |
$6$ |
$2$ |
$1$ |
$0.642$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{6}-\zeta_{6}^{2}q^{7}+\cdots\) |
1287.1.ba.b |
$1287$ |
$1$ |
1287.ba |
1287.aa |
$6$ |
$2$ |
$1$ |
$0.642$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{6}+\zeta_{6}^{2}q^{7}+\cdots\) |
1287.1.ba.c |
$1287$ |
$1$ |
1287.ba |
1287.aa |
$6$ |
$8$ |
$4$ |
$0.642$ |
\(\Q(\zeta_{15})\) |
$D_{15}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}-\zeta_{30}^{11}q^{3}+(\zeta_{30}^{8}+\cdots)q^{4}+\cdots\) |
1287.1.ba.d |
$1287$ |
$1$ |
1287.ba |
1287.aa |
$6$ |
$8$ |
$4$ |
$0.642$ |
\(\Q(\zeta_{15})\) |
$D_{15}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}-\zeta_{30}^{11}q^{3}+\cdots\) |
1573.1.l.a |
$1573$ |
$1$ |
1573.l |
143.l |
$10$ |
$4$ |
$1$ |
$0.785$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-3\) |
\(-2\) |
\(0\) |
\(-3\) |
$1$ |
|
\(q+(-1+\zeta_{10}^{3})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{3}+\cdots\) |
1573.1.l.b |
$1573$ |
$1$ |
1573.l |
143.l |
$10$ |
$4$ |
$1$ |
$0.785$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-2\) |
\(3\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(1+\zeta_{10}^{4})q^{3}+\cdots\) |
1573.1.l.c |
$1573$ |
$1$ |
1573.l |
143.l |
$10$ |
$4$ |
$1$ |
$0.785$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(2\) |
\(3\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(1+\zeta_{10}^{4})q^{3}+\cdots\) |
1573.1.l.d |
$1573$ |
$1$ |
1573.l |
143.l |
$10$ |
$4$ |
$1$ |
$0.785$ |
\(\Q(\zeta_{10})\) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(3\) |
\(-2\) |
\(0\) |
\(3\) |
$1$ |
|
\(q+(1-\zeta_{10}^{3})q^{2}+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\) |
1716.1.m.a |
$1716$ |
$1$ |
1716.m |
1716.m |
$2$ |
$1$ |
$1$ |
$0.856$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-429}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\) |
1716.1.m.b |
$1716$ |
$1$ |
1716.m |
1716.m |
$2$ |
$1$ |
$1$ |
$0.856$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-429}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\) |
1716.1.m.c |
$1716$ |
$1$ |
1716.m |
1716.m |
$2$ |
$1$ |
$1$ |
$0.856$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-429}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\) |
1716.1.m.d |
$1716$ |
$1$ |
1716.m |
1716.m |
$2$ |
$1$ |
$1$ |
$0.856$ |
\(\Q\) |
$D_{2}$ |
\(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-429}) \) |
\(\Q(\sqrt{3}) \) |
✓ |
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\) |
1716.1.m.e |
$1716$ |
$1$ |
1716.m |
1716.m |
$2$ |
$4$ |
$4$ |
$0.856$ |
\(\Q(\zeta_{10})\) |
$D_{10}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{10}^{2}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots\) |
1716.1.m.f |
$1716$ |
$1$ |
1716.m |
1716.m |
$2$ |
$4$ |
$4$ |
$0.856$ |
\(\Q(\zeta_{10})\) |
$D_{10}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{10}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{2}q^{6}+\cdots\) |
1716.1.m.i |
$1716$ |
$1$ |
1716.m |
1716.m |
$2$ |
$4$ |
$4$ |
$0.856$ |
\(\Q(\zeta_{10})\) |
$D_{10}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{10}^{2}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots\) |
1716.1.m.j |
$1716$ |
$1$ |
1716.m |
1716.m |
$2$ |
$4$ |
$4$ |
$0.856$ |
\(\Q(\zeta_{10})\) |
$D_{10}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+\zeta_{10}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{2}q^{6}+\cdots\) |
1859.1.c.c |
$1859$ |
$1$ |
1859.c |
11.b |
$2$ |
$4$ |
$4$ |
$0.928$ |
\(\Q(i, \sqrt{5})\) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{6}+\cdots\) |
1859.1.i.a |
$1859$ |
$1$ |
1859.i |
143.i |
$6$ |
$4$ |
$2$ |
$0.928$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\) |
1859.1.i.b |
$1859$ |
$1$ |
1859.i |
143.i |
$6$ |
$4$ |
$2$ |
$0.928$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\) |
1859.1.k.c |
$1859$ |
$1$ |
1859.k |
143.k |
$6$ |
$8$ |
$4$ |
$0.928$ |
8.0.12960000.1 |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(-\beta _{3}-\beta _{6}-\beta _{7})q^{2}+(1-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\) |
2288.1.m.a |
$2288$ |
$1$ |
2288.m |
143.d |
$2$ |
$2$ |
$2$ |
$1.142$ |
\(\Q(\sqrt{5}) \) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(-1\) |
$1$ |
|
\(q+\beta q^{3}+(-1+\beta )q^{7}+\beta q^{9}+q^{11}+\cdots\) |
2288.1.m.b |
$2288$ |
$1$ |
2288.m |
143.d |
$2$ |
$2$ |
$2$ |
$1.142$ |
\(\Q(\sqrt{5}) \) |
$D_{5}$ |
\(\Q(\sqrt{-143}) \) |
None |
✓ |
$2$ |
$0$ |
\(0\) |
\(1\) |
\(0\) |
\(1\) |
$1$ |
|
\(q+\beta q^{3}+(1-\beta )q^{7}+\beta q^{9}-q^{11}+q^{13}+\cdots\) |
2288.1.z.a |
$2288$ |
$1$ |
2288.z |
2288.z |
$4$ |
$4$ |
$2$ |
$1.142$ |
\(\Q(\zeta_{8})\) |
$D_{4}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{8}^{3}q^{2}+(1+\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\) |
2288.1.z.b |
$2288$ |
$1$ |
2288.z |
2288.z |
$4$ |
$16$ |
$8$ |
$1.142$ |
\(\Q(\zeta_{40})\) |
$D_{20}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{40}^{11}q^{2}+(-\zeta_{40}^{14}+\zeta_{40}^{16}+\cdots)q^{3}+\cdots\) |
2717.1.x.a |
$2717$ |
$1$ |
2717.x |
2717.x |
$6$ |
$2$ |
$1$ |
$1.356$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(1\) |
\(0\) |
\(2\) |
$1$ |
|
\(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{6}+q^{7}-q^{8}+\cdots\) |
2717.1.x.b |
$2717$ |
$1$ |
2717.x |
2717.x |
$6$ |
$2$ |
$1$ |
$1.356$ |
\(\Q(\sqrt{-3}) \) |
$D_{3}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{6}-q^{7}+q^{8}+\cdots\) |
2717.1.x.c |
$2717$ |
$1$ |
2717.x |
2717.x |
$6$ |
$8$ |
$4$ |
$1.356$ |
\(\Q(\zeta_{15})\) |
$D_{15}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-1\) |
\(-1\) |
\(0\) |
\(2\) |
$1$ |
|
\(q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(\zeta_{30}^{2}-\zeta_{30}^{3}+\cdots)q^{3}+\cdots\) |
2717.1.x.d |
$2717$ |
$1$ |
2717.x |
2717.x |
$6$ |
$8$ |
$4$ |
$1.356$ |
\(\Q(\zeta_{15})\) |
$D_{15}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(1\) |
\(-1\) |
\(0\) |
\(-2\) |
$1$ |
|
\(q+(-\zeta_{30}^{6}-\zeta_{30}^{14})q^{2}+(-\zeta_{30}^{9}+\cdots)q^{3}+\cdots\) |
2717.1.db.a |
$2717$ |
$1$ |
2717.db |
2717.cb |
$18$ |
$6$ |
$1$ |
$1.356$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-3\) |
\(-3\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(-\zeta_{18}^{3}+\zeta_{18}^{8})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{6}+\cdots)q^{3}+\cdots\) |
2717.1.db.b |
$2717$ |
$1$ |
2717.db |
2717.cb |
$18$ |
$6$ |
$1$ |
$1.356$ |
\(\Q(\zeta_{18})\) |
$D_{9}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(3\) |
\(-3\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(\zeta_{18}^{3}-\zeta_{18}^{8})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{6}+\cdots)q^{3}+\cdots\) |
2717.1.db.c |
$2717$ |
$1$ |
2717.db |
2717.cb |
$18$ |
$24$ |
$4$ |
$1.356$ |
\(\Q(\zeta_{45})\) |
$D_{45}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(-3\) |
\(3\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(\zeta_{90}^{11}+\zeta_{90}^{39})q^{2}+(\zeta_{90}^{6}+\zeta_{90}^{14}+\cdots)q^{3}+\cdots\) |
2717.1.db.d |
$2717$ |
$1$ |
2717.db |
2717.cb |
$18$ |
$24$ |
$4$ |
$1.356$ |
\(\Q(\zeta_{45})\) |
$D_{45}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$4$ |
$0$ |
\(3\) |
\(3\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(-\zeta_{90}^{11}-\zeta_{90}^{39})q^{2}+(\zeta_{90}^{6}+\zeta_{90}^{14}+\cdots)q^{3}+\cdots\) |
3003.1.b.a |
$3003$ |
$1$ |
3003.b |
3003.b |
$2$ |
$2$ |
$2$ |
$1.499$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-231}) \) |
\(\Q(\sqrt{273}) \) |
|
$8$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}-q^{3}-3q^{4}+2iq^{6}-iq^{7}+\cdots\) |
3003.1.b.b |
$3003$ |
$1$ |
3003.b |
3003.b |
$2$ |
$2$ |
$2$ |
$1.499$ |
\(\Q(\sqrt{-1}) \) |
$D_{2}$ |
\(\Q(\sqrt{-143}) \), \(\Q(\sqrt{-231}) \) |
\(\Q(\sqrt{273}) \) |
|
$8$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-iq^{2}+q^{3}-3q^{4}-2iq^{6}+iq^{7}+\cdots\) |
3003.1.b.e |
$3003$ |
$1$ |
3003.b |
3003.b |
$2$ |
$8$ |
$8$ |
$1.499$ |
\(\Q(\zeta_{20})\) |
$D_{10}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(\zeta_{20}+\zeta_{20}^{9})q^{2}+\zeta_{20}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots\) |
3003.1.b.f |
$3003$ |
$1$ |
3003.b |
3003.b |
$2$ |
$8$ |
$8$ |
$1.499$ |
\(\Q(\zeta_{20})\) |
$D_{10}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(\zeta_{20}+\zeta_{20}^{9})q^{2}-\zeta_{20}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots\) |
3003.1.cv.a |
$3003$ |
$1$ |
3003.cv |
3003.bv |
$6$ |
$4$ |
$2$ |
$1.499$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(-4\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{5}q^{2}-q^{3}+\zeta_{12}^{5}q^{6}+\zeta_{12}q^{7}+\cdots\) |
3003.1.cv.b |
$3003$ |
$1$ |
3003.cv |
3003.bv |
$6$ |
$4$ |
$2$ |
$1.499$ |
\(\Q(\zeta_{12})\) |
$D_{6}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(-2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{6}-\zeta_{12}q^{7}+\cdots\) |
3003.1.cv.c |
$3003$ |
$1$ |
3003.cv |
3003.bv |
$6$ |
$16$ |
$8$ |
$1.499$ |
\(\Q(\zeta_{60})\) |
$D_{30}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(2\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(-\zeta_{60}^{21}-\zeta_{60}^{29})q^{2}+\zeta_{60}^{4}q^{3}+\cdots\) |
3003.1.cv.d |
$3003$ |
$1$ |
3003.cv |
3003.bv |
$6$ |
$16$ |
$8$ |
$1.499$ |
\(\Q(\zeta_{60})\) |
$D_{30}$ |
\(\Q(\sqrt{-143}) \) |
None |
|
$8$ |
$0$ |
\(0\) |
\(4\) |
\(0\) |
\(0\) |
$1$ |
|
\(q+(\zeta_{60}^{3}+\zeta_{60}^{7})q^{2}+\zeta_{60}^{18}q^{3}+(\zeta_{60}^{6}+\cdots)q^{4}+\cdots\) |