Basic properties
| Modulus: | \(259200\) | |
| Conductor: | \(25920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(432\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{25920}(21067,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 259200.vg
\(\chi_{259200}(7,\cdot)\) \(\chi_{259200}(2407,\cdot)\) \(\chi_{259200}(2743,\cdot)\) \(\chi_{259200}(5143,\cdot)\) \(\chi_{259200}(7207,\cdot)\) \(\chi_{259200}(9607,\cdot)\) \(\chi_{259200}(9943,\cdot)\) \(\chi_{259200}(12343,\cdot)\) \(\chi_{259200}(14407,\cdot)\) \(\chi_{259200}(16807,\cdot)\) \(\chi_{259200}(17143,\cdot)\) \(\chi_{259200}(19543,\cdot)\) \(\chi_{259200}(21607,\cdot)\) \(\chi_{259200}(24007,\cdot)\) \(\chi_{259200}(24343,\cdot)\) \(\chi_{259200}(26743,\cdot)\) \(\chi_{259200}(28807,\cdot)\) \(\chi_{259200}(31207,\cdot)\) \(\chi_{259200}(31543,\cdot)\) \(\chi_{259200}(33943,\cdot)\) \(\chi_{259200}(36007,\cdot)\) \(\chi_{259200}(38407,\cdot)\) \(\chi_{259200}(38743,\cdot)\) \(\chi_{259200}(41143,\cdot)\) \(\chi_{259200}(43207,\cdot)\) \(\chi_{259200}(45607,\cdot)\) \(\chi_{259200}(45943,\cdot)\) \(\chi_{259200}(48343,\cdot)\) \(\chi_{259200}(50407,\cdot)\) \(\chi_{259200}(52807,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{432})$ |
| Fixed field: | Number field defined by a degree 432 polynomial (not computed) |
Values on generators
\((157951,202501,6401,72577)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{8}{27}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 259200 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{133}{216}\right)\) | \(e\left(\frac{395}{432}\right)\) | \(e\left(\frac{349}{432}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{59}{144}\right)\) | \(e\left(\frac{191}{216}\right)\) | \(e\left(\frac{389}{432}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{73}{144}\right)\) | \(e\left(\frac{17}{216}\right)\) |