Basic properties
| Modulus: | \(2304\) | |
| Conductor: | \(2304\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(192\) | 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 2304.cc
\(\chi_{2304}(43,\cdot)\) \(\chi_{2304}(67,\cdot)\) \(\chi_{2304}(115,\cdot)\) \(\chi_{2304}(139,\cdot)\) \(\chi_{2304}(187,\cdot)\) \(\chi_{2304}(211,\cdot)\) \(\chi_{2304}(259,\cdot)\) \(\chi_{2304}(283,\cdot)\) \(\chi_{2304}(331,\cdot)\) \(\chi_{2304}(355,\cdot)\) \(\chi_{2304}(403,\cdot)\) \(\chi_{2304}(427,\cdot)\) \(\chi_{2304}(475,\cdot)\) \(\chi_{2304}(499,\cdot)\) \(\chi_{2304}(547,\cdot)\) \(\chi_{2304}(571,\cdot)\) \(\chi_{2304}(619,\cdot)\) \(\chi_{2304}(643,\cdot)\) \(\chi_{2304}(691,\cdot)\) \(\chi_{2304}(715,\cdot)\) \(\chi_{2304}(763,\cdot)\) \(\chi_{2304}(787,\cdot)\) \(\chi_{2304}(835,\cdot)\) \(\chi_{2304}(859,\cdot)\) \(\chi_{2304}(907,\cdot)\) \(\chi_{2304}(931,\cdot)\) \(\chi_{2304}(979,\cdot)\) \(\chi_{2304}(1003,\cdot)\) \(\chi_{2304}(1051,\cdot)\) \(\chi_{2304}(1075,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1279,2053,1793)\) → \((-1,e\left(\frac{5}{64}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2304 }(715, a) \) | \(-1\) | \(1\) | \(e\left(\frac{143}{192}\right)\) | \(e\left(\frac{59}{96}\right)\) | \(e\left(\frac{91}{192}\right)\) | \(e\left(\frac{65}{192}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{181}{192}\right)\) | \(e\left(\frac{19}{24}\right)\) |