Basic properties
| Modulus: | \(5184\) | |
| Conductor: | \(5184\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5184.cz
\(\chi_{5184}(43,\cdot)\) \(\chi_{5184}(67,\cdot)\) \(\chi_{5184}(115,\cdot)\) \(\chi_{5184}(139,\cdot)\) \(\chi_{5184}(187,\cdot)\) \(\chi_{5184}(211,\cdot)\) \(\chi_{5184}(259,\cdot)\) \(\chi_{5184}(283,\cdot)\) \(\chi_{5184}(331,\cdot)\) \(\chi_{5184}(355,\cdot)\) \(\chi_{5184}(403,\cdot)\) \(\chi_{5184}(427,\cdot)\) \(\chi_{5184}(475,\cdot)\) \(\chi_{5184}(499,\cdot)\) \(\chi_{5184}(547,\cdot)\) \(\chi_{5184}(571,\cdot)\) \(\chi_{5184}(619,\cdot)\) \(\chi_{5184}(643,\cdot)\) \(\chi_{5184}(691,\cdot)\) \(\chi_{5184}(715,\cdot)\) \(\chi_{5184}(763,\cdot)\) \(\chi_{5184}(787,\cdot)\) \(\chi_{5184}(835,\cdot)\) \(\chi_{5184}(859,\cdot)\) \(\chi_{5184}(907,\cdot)\) \(\chi_{5184}(931,\cdot)\) \(\chi_{5184}(979,\cdot)\) \(\chi_{5184}(1003,\cdot)\) \(\chi_{5184}(1051,\cdot)\) \(\chi_{5184}(1075,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{432})$ |
| Fixed field: | Number field defined by a degree 432 polynomial (not computed) |
Values on generators
\((2431,325,1217)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{11}{27}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 5184 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{432}\right)\) | \(e\left(\frac{31}{216}\right)\) | \(e\left(\frac{371}{432}\right)\) | \(e\left(\frac{193}{432}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{107}{144}\right)\) | \(e\left(\frac{77}{216}\right)\) | \(e\left(\frac{79}{216}\right)\) | \(e\left(\frac{5}{432}\right)\) | \(e\left(\frac{4}{27}\right)\) |