Basic properties
| Modulus: | \(7935\) | |
| Conductor: | \(529\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(23\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{529}(346,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7935.u
\(\chi_{7935}(346,\cdot)\) \(\chi_{7935}(691,\cdot)\) \(\chi_{7935}(1036,\cdot)\) \(\chi_{7935}(1381,\cdot)\) \(\chi_{7935}(1726,\cdot)\) \(\chi_{7935}(2071,\cdot)\) \(\chi_{7935}(2416,\cdot)\) \(\chi_{7935}(2761,\cdot)\) \(\chi_{7935}(3106,\cdot)\) \(\chi_{7935}(3451,\cdot)\) \(\chi_{7935}(3796,\cdot)\) \(\chi_{7935}(4141,\cdot)\) \(\chi_{7935}(4486,\cdot)\) \(\chi_{7935}(4831,\cdot)\) \(\chi_{7935}(5176,\cdot)\) \(\chi_{7935}(5521,\cdot)\) \(\chi_{7935}(5866,\cdot)\) \(\chi_{7935}(6211,\cdot)\) \(\chi_{7935}(6556,\cdot)\) \(\chi_{7935}(6901,\cdot)\) \(\chi_{7935}(7246,\cdot)\) \(\chi_{7935}(7591,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{23})\) |
| Fixed field: | Number field defined by a degree 23 polynomial |
Values on generators
\((5291,4762,7411)\) → \((1,1,e\left(\frac{6}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 7935 }(346, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) |