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.cb
\(\chi_{2304}(5,\cdot)\) \(\chi_{2304}(29,\cdot)\) \(\chi_{2304}(77,\cdot)\) \(\chi_{2304}(101,\cdot)\) \(\chi_{2304}(149,\cdot)\) \(\chi_{2304}(173,\cdot)\) \(\chi_{2304}(221,\cdot)\) \(\chi_{2304}(245,\cdot)\) \(\chi_{2304}(293,\cdot)\) \(\chi_{2304}(317,\cdot)\) \(\chi_{2304}(365,\cdot)\) \(\chi_{2304}(389,\cdot)\) \(\chi_{2304}(437,\cdot)\) \(\chi_{2304}(461,\cdot)\) \(\chi_{2304}(509,\cdot)\) \(\chi_{2304}(533,\cdot)\) \(\chi_{2304}(581,\cdot)\) \(\chi_{2304}(605,\cdot)\) \(\chi_{2304}(653,\cdot)\) \(\chi_{2304}(677,\cdot)\) \(\chi_{2304}(725,\cdot)\) \(\chi_{2304}(749,\cdot)\) \(\chi_{2304}(797,\cdot)\) \(\chi_{2304}(821,\cdot)\) \(\chi_{2304}(869,\cdot)\) \(\chi_{2304}(893,\cdot)\) \(\chi_{2304}(941,\cdot)\) \(\chi_{2304}(965,\cdot)\) \(\chi_{2304}(1013,\cdot)\) \(\chi_{2304}(1037,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{192})$ |
| Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1279,2053,1793)\) → \((1,e\left(\frac{43}{64}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2304 }(605, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{192}\right)\) | \(e\left(\frac{37}{96}\right)\) | \(e\left(\frac{53}{192}\right)\) | \(e\left(\frac{175}{192}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{1}{96}\right)\) | \(e\left(\frac{155}{192}\right)\) | \(e\left(\frac{17}{24}\right)\) |