Basic properties
| Modulus: | \(7935\) | |
| Conductor: | \(1587\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(506\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1587}(356,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7935.bm
\(\chi_{7935}(11,\cdot)\) \(\chi_{7935}(56,\cdot)\) \(\chi_{7935}(86,\cdot)\) \(\chi_{7935}(176,\cdot)\) \(\chi_{7935}(191,\cdot)\) \(\chi_{7935}(221,\cdot)\) \(\chi_{7935}(251,\cdot)\) \(\chi_{7935}(281,\cdot)\) \(\chi_{7935}(296,\cdot)\) \(\chi_{7935}(341,\cdot)\) \(\chi_{7935}(356,\cdot)\) \(\chi_{7935}(401,\cdot)\) \(\chi_{7935}(431,\cdot)\) \(\chi_{7935}(521,\cdot)\) \(\chi_{7935}(536,\cdot)\) \(\chi_{7935}(566,\cdot)\) \(\chi_{7935}(596,\cdot)\) \(\chi_{7935}(626,\cdot)\) \(\chi_{7935}(641,\cdot)\) \(\chi_{7935}(686,\cdot)\) \(\chi_{7935}(701,\cdot)\) \(\chi_{7935}(746,\cdot)\) \(\chi_{7935}(776,\cdot)\) \(\chi_{7935}(866,\cdot)\) \(\chi_{7935}(911,\cdot)\) \(\chi_{7935}(941,\cdot)\) \(\chi_{7935}(971,\cdot)\) \(\chi_{7935}(986,\cdot)\) \(\chi_{7935}(1031,\cdot)\) \(\chi_{7935}(1046,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 506 polynomial (not computed) |
Values on generators
\((5291,4762,7411)\) → \((-1,1,e\left(\frac{185}{506}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 7935 }(356, a) \) | \(1\) | \(1\) | \(e\left(\frac{315}{506}\right)\) | \(e\left(\frac{62}{253}\right)\) | \(e\left(\frac{83}{506}\right)\) | \(e\left(\frac{439}{506}\right)\) | \(e\left(\frac{167}{253}\right)\) | \(e\left(\frac{118}{253}\right)\) | \(e\left(\frac{199}{253}\right)\) | \(e\left(\frac{124}{253}\right)\) | \(e\left(\frac{26}{253}\right)\) | \(e\left(\frac{223}{506}\right)\) |