Basic properties
| Modulus: | \(2592\) | |
| Conductor: | \(2592\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(216\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2592.ci
\(\chi_{2592}(11,\cdot)\) \(\chi_{2592}(59,\cdot)\) \(\chi_{2592}(83,\cdot)\) \(\chi_{2592}(131,\cdot)\) \(\chi_{2592}(155,\cdot)\) \(\chi_{2592}(203,\cdot)\) \(\chi_{2592}(227,\cdot)\) \(\chi_{2592}(275,\cdot)\) \(\chi_{2592}(299,\cdot)\) \(\chi_{2592}(347,\cdot)\) \(\chi_{2592}(371,\cdot)\) \(\chi_{2592}(419,\cdot)\) \(\chi_{2592}(443,\cdot)\) \(\chi_{2592}(491,\cdot)\) \(\chi_{2592}(515,\cdot)\) \(\chi_{2592}(563,\cdot)\) \(\chi_{2592}(587,\cdot)\) \(\chi_{2592}(635,\cdot)\) \(\chi_{2592}(659,\cdot)\) \(\chi_{2592}(707,\cdot)\) \(\chi_{2592}(731,\cdot)\) \(\chi_{2592}(779,\cdot)\) \(\chi_{2592}(803,\cdot)\) \(\chi_{2592}(851,\cdot)\) \(\chi_{2592}(875,\cdot)\) \(\chi_{2592}(923,\cdot)\) \(\chi_{2592}(947,\cdot)\) \(\chi_{2592}(995,\cdot)\) \(\chi_{2592}(1019,\cdot)\) \(\chi_{2592}(1067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{216})$ |
| Fixed field: | Number field defined by a degree 216 polynomial (not computed) |
Values on generators
\((2431,325,1217)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{13}{54}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2592 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{216}\right)\) | \(e\left(\frac{65}{108}\right)\) | \(e\left(\frac{163}{216}\right)\) | \(e\left(\frac{65}{216}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{35}{108}\right)\) | \(e\left(\frac{169}{216}\right)\) | \(e\left(\frac{17}{54}\right)\) |