Basic properties
| Modulus: | \(25920\) | |
| Conductor: | \(25920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(432\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 25920.km
\(\chi_{25920}(187,\cdot)\) \(\chi_{25920}(403,\cdot)\) \(\chi_{25920}(427,\cdot)\) \(\chi_{25920}(643,\cdot)\) \(\chi_{25920}(907,\cdot)\) \(\chi_{25920}(1123,\cdot)\) \(\chi_{25920}(1147,\cdot)\) \(\chi_{25920}(1363,\cdot)\) \(\chi_{25920}(1627,\cdot)\) \(\chi_{25920}(1843,\cdot)\) \(\chi_{25920}(1867,\cdot)\) \(\chi_{25920}(2083,\cdot)\) \(\chi_{25920}(2347,\cdot)\) \(\chi_{25920}(2563,\cdot)\) \(\chi_{25920}(2587,\cdot)\) \(\chi_{25920}(2803,\cdot)\) \(\chi_{25920}(3067,\cdot)\) \(\chi_{25920}(3283,\cdot)\) \(\chi_{25920}(3307,\cdot)\) \(\chi_{25920}(3523,\cdot)\) \(\chi_{25920}(3787,\cdot)\) \(\chi_{25920}(4003,\cdot)\) \(\chi_{25920}(4027,\cdot)\) \(\chi_{25920}(4243,\cdot)\) \(\chi_{25920}(4507,\cdot)\) \(\chi_{25920}(4723,\cdot)\) \(\chi_{25920}(4747,\cdot)\) \(\chi_{25920}(4963,\cdot)\) \(\chi_{25920}(5227,\cdot)\) \(\chi_{25920}(5443,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{432})$ |
| Fixed field: | Number field defined by a degree 432 polynomial (not computed) |
Values on generators
\((2431,21061,6401,20737)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{8}{27}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 25920 }(21067, a) \) | \(1\) | \(1\) | \(e\left(\frac{133}{216}\right)\) | \(e\left(\frac{395}{432}\right)\) | \(e\left(\frac{349}{432}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{59}{144}\right)\) | \(e\left(\frac{191}{216}\right)\) | \(e\left(\frac{389}{432}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{73}{144}\right)\) | \(e\left(\frac{17}{216}\right)\) |