Basic properties
| Modulus: | \(5376\) | |
| Conductor: | \(1792\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1792}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5376.eh
\(\chi_{5376}(19,\cdot)\) \(\chi_{5376}(115,\cdot)\) \(\chi_{5376}(187,\cdot)\) \(\chi_{5376}(283,\cdot)\) \(\chi_{5376}(355,\cdot)\) \(\chi_{5376}(451,\cdot)\) \(\chi_{5376}(523,\cdot)\) \(\chi_{5376}(619,\cdot)\) \(\chi_{5376}(691,\cdot)\) \(\chi_{5376}(787,\cdot)\) \(\chi_{5376}(859,\cdot)\) \(\chi_{5376}(955,\cdot)\) \(\chi_{5376}(1027,\cdot)\) \(\chi_{5376}(1123,\cdot)\) \(\chi_{5376}(1195,\cdot)\) \(\chi_{5376}(1291,\cdot)\) \(\chi_{5376}(1363,\cdot)\) \(\chi_{5376}(1459,\cdot)\) \(\chi_{5376}(1531,\cdot)\) \(\chi_{5376}(1627,\cdot)\) \(\chi_{5376}(1699,\cdot)\) \(\chi_{5376}(1795,\cdot)\) \(\chi_{5376}(1867,\cdot)\) \(\chi_{5376}(1963,\cdot)\) \(\chi_{5376}(2035,\cdot)\) \(\chi_{5376}(2131,\cdot)\) \(\chi_{5376}(2203,\cdot)\) \(\chi_{5376}(2299,\cdot)\) \(\chi_{5376}(2371,\cdot)\) \(\chi_{5376}(2467,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((2815,5125,1793,4609)\) → \((-1,e\left(\frac{23}{64}\right),1,e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5376 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{192}\right)\) | \(e\left(\frac{73}{192}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{179}{192}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{125}{192}\right)\) |