Basic properties
| Modulus: | \(5184\) | |
| Conductor: | \(2592\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(216\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2592}(2291,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5184.cu
\(\chi_{5184}(23,\cdot)\) \(\chi_{5184}(119,\cdot)\) \(\chi_{5184}(167,\cdot)\) \(\chi_{5184}(263,\cdot)\) \(\chi_{5184}(311,\cdot)\) \(\chi_{5184}(407,\cdot)\) \(\chi_{5184}(455,\cdot)\) \(\chi_{5184}(551,\cdot)\) \(\chi_{5184}(599,\cdot)\) \(\chi_{5184}(695,\cdot)\) \(\chi_{5184}(743,\cdot)\) \(\chi_{5184}(839,\cdot)\) \(\chi_{5184}(887,\cdot)\) \(\chi_{5184}(983,\cdot)\) \(\chi_{5184}(1031,\cdot)\) \(\chi_{5184}(1127,\cdot)\) \(\chi_{5184}(1175,\cdot)\) \(\chi_{5184}(1271,\cdot)\) \(\chi_{5184}(1319,\cdot)\) \(\chi_{5184}(1415,\cdot)\) \(\chi_{5184}(1463,\cdot)\) \(\chi_{5184}(1559,\cdot)\) \(\chi_{5184}(1607,\cdot)\) \(\chi_{5184}(1703,\cdot)\) \(\chi_{5184}(1751,\cdot)\) \(\chi_{5184}(1847,\cdot)\) \(\chi_{5184}(1895,\cdot)\) \(\chi_{5184}(1991,\cdot)\) \(\chi_{5184}(2039,\cdot)\) \(\chi_{5184}(2135,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{216})$ |
| Fixed field: | Number field defined by a degree 216 polynomial (not computed) |
Values on generators
\((2431,325,1217)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{11}{54}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 5184 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{121}{216}\right)\) | \(e\left(\frac{55}{108}\right)\) | \(e\left(\frac{113}{216}\right)\) | \(e\left(\frac{163}{216}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{35}{216}\right)\) | \(e\left(\frac{31}{54}\right)\) |