Basic properties
| Modulus: | \(2432\) | |
| Conductor: | \(1216\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1216}(309,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2432.co
\(\chi_{2432}(9,\cdot)\) \(\chi_{2432}(25,\cdot)\) \(\chi_{2432}(73,\cdot)\) \(\chi_{2432}(137,\cdot)\) \(\chi_{2432}(169,\cdot)\) \(\chi_{2432}(233,\cdot)\) \(\chi_{2432}(313,\cdot)\) \(\chi_{2432}(329,\cdot)\) \(\chi_{2432}(377,\cdot)\) \(\chi_{2432}(441,\cdot)\) \(\chi_{2432}(473,\cdot)\) \(\chi_{2432}(537,\cdot)\) \(\chi_{2432}(617,\cdot)\) \(\chi_{2432}(633,\cdot)\) \(\chi_{2432}(681,\cdot)\) \(\chi_{2432}(745,\cdot)\) \(\chi_{2432}(777,\cdot)\) \(\chi_{2432}(841,\cdot)\) \(\chi_{2432}(921,\cdot)\) \(\chi_{2432}(937,\cdot)\) \(\chi_{2432}(985,\cdot)\) \(\chi_{2432}(1049,\cdot)\) \(\chi_{2432}(1081,\cdot)\) \(\chi_{2432}(1145,\cdot)\) \(\chi_{2432}(1225,\cdot)\) \(\chi_{2432}(1241,\cdot)\) \(\chi_{2432}(1289,\cdot)\) \(\chi_{2432}(1353,\cdot)\) \(\chi_{2432}(1385,\cdot)\) \(\chi_{2432}(1449,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((1407,2053,1921)\) → \((1,e\left(\frac{5}{16}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2432 }(1145, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{144}\right)\) | \(e\left(\frac{77}{144}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{71}{72}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{19}{144}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{137}{144}\right)\) | \(e\left(\frac{11}{72}\right)\) |