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 \(\chi_{608}(397,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2432.ce
\(\chi_{2432}(17,\cdot)\) \(\chi_{2432}(81,\cdot)\) \(\chi_{2432}(177,\cdot)\) \(\chi_{2432}(465,\cdot)\) \(\chi_{2432}(529,\cdot)\) \(\chi_{2432}(593,\cdot)\) \(\chi_{2432}(625,\cdot)\) \(\chi_{2432}(689,\cdot)\) \(\chi_{2432}(785,\cdot)\) \(\chi_{2432}(1073,\cdot)\) \(\chi_{2432}(1137,\cdot)\) \(\chi_{2432}(1201,\cdot)\) \(\chi_{2432}(1233,\cdot)\) \(\chi_{2432}(1297,\cdot)\) \(\chi_{2432}(1393,\cdot)\) \(\chi_{2432}(1681,\cdot)\) \(\chi_{2432}(1745,\cdot)\) \(\chi_{2432}(1809,\cdot)\) \(\chi_{2432}(1841,\cdot)\) \(\chi_{2432}(1905,\cdot)\) \(\chi_{2432}(2001,\cdot)\) \(\chi_{2432}(2289,\cdot)\) \(\chi_{2432}(2353,\cdot)\) \(\chi_{2432}(2417,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((1407,2053,1921)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{67}{72}\right)\) | \(e\left(\frac{13}{36}\right)\) |