Basic properties
| Modulus: | \(30148\) | |
| Conductor: | \(30148\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1884\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 30148.bg
\(\chi_{30148}(3,\cdot)\) \(\chi_{30148}(35,\cdot)\) \(\chi_{30148}(103,\cdot)\) \(\chi_{30148}(119,\cdot)\) \(\chi_{30148}(215,\cdot)\) \(\chi_{30148}(231,\cdot)\) \(\chi_{30148}(243,\cdot)\) \(\chi_{30148}(251,\cdot)\) \(\chi_{30148}(283,\cdot)\) \(\chi_{30148}(311,\cdot)\) \(\chi_{30148}(315,\cdot)\) \(\chi_{30148}(415,\cdot)\) \(\chi_{30148}(451,\cdot)\) \(\chi_{30148}(615,\cdot)\) \(\chi_{30148}(631,\cdot)\) \(\chi_{30148}(731,\cdot)\) \(\chi_{30148}(843,\cdot)\) \(\chi_{30148}(927,\cdot)\) \(\chi_{30148}(983,\cdot)\) \(\chi_{30148}(1039,\cdot)\) \(\chi_{30148}(1055,\cdot)\) \(\chi_{30148}(1071,\cdot)\) \(\chi_{30148}(1147,\cdot)\) \(\chi_{30148}(1411,\cdot)\) \(\chi_{30148}(1419,\cdot)\) \(\chi_{30148}(1423,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1884})$ |
| Fixed field: | Number field defined by a degree 1884 polynomial (not computed) |
Values on generators
\((15075,15081)\) → \((-1,e\left(\frac{425}{1884}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 30148 }(315, a) \) | \(-1\) | \(1\) | \(e\left(\frac{251}{942}\right)\) | \(e\left(\frac{461}{628}\right)\) | \(e\left(\frac{1367}{1884}\right)\) | \(e\left(\frac{251}{471}\right)\) | \(e\left(\frac{521}{1884}\right)\) | \(e\left(\frac{415}{942}\right)\) | \(e\left(\frac{1}{1884}\right)\) | \(e\left(\frac{621}{628}\right)\) | \(e\left(\frac{889}{1884}\right)\) | \(e\left(\frac{623}{628}\right)\) |