Basic properties
| Modulus: | \(2432\) | |
| Conductor: | \(608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{608}(91,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2432.cf
\(\chi_{2432}(15,\cdot)\) \(\chi_{2432}(79,\cdot)\) \(\chi_{2432}(143,\cdot)\) \(\chi_{2432}(431,\cdot)\) \(\chi_{2432}(527,\cdot)\) \(\chi_{2432}(591,\cdot)\) \(\chi_{2432}(623,\cdot)\) \(\chi_{2432}(687,\cdot)\) \(\chi_{2432}(751,\cdot)\) \(\chi_{2432}(1039,\cdot)\) \(\chi_{2432}(1135,\cdot)\) \(\chi_{2432}(1199,\cdot)\) \(\chi_{2432}(1231,\cdot)\) \(\chi_{2432}(1295,\cdot)\) \(\chi_{2432}(1359,\cdot)\) \(\chi_{2432}(1647,\cdot)\) \(\chi_{2432}(1743,\cdot)\) \(\chi_{2432}(1807,\cdot)\) \(\chi_{2432}(1839,\cdot)\) \(\chi_{2432}(1903,\cdot)\) \(\chi_{2432}(1967,\cdot)\) \(\chi_{2432}(2255,\cdot)\) \(\chi_{2432}(2351,\cdot)\) \(\chi_{2432}(2415,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((1407,2053,1921)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{17}{36}\right)\) |