Basic properties
| Modulus: | \(1328\) | |
| Conductor: | \(1328\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(164\) | 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 1328.v
\(\chi_{1328}(3,\cdot)\) \(\chi_{1328}(11,\cdot)\) \(\chi_{1328}(27,\cdot)\) \(\chi_{1328}(51,\cdot)\) \(\chi_{1328}(59,\cdot)\) \(\chi_{1328}(75,\cdot)\) \(\chi_{1328}(99,\cdot)\) \(\chi_{1328}(123,\cdot)\) \(\chi_{1328}(131,\cdot)\) \(\chi_{1328}(147,\cdot)\) \(\chi_{1328}(187,\cdot)\) \(\chi_{1328}(195,\cdot)\) \(\chi_{1328}(203,\cdot)\) \(\chi_{1328}(227,\cdot)\) \(\chi_{1328}(235,\cdot)\) \(\chi_{1328}(243,\cdot)\) \(\chi_{1328}(259,\cdot)\) \(\chi_{1328}(275,\cdot)\) \(\chi_{1328}(339,\cdot)\) \(\chi_{1328}(355,\cdot)\) \(\chi_{1328}(363,\cdot)\) \(\chi_{1328}(395,\cdot)\) \(\chi_{1328}(419,\cdot)\) \(\chi_{1328}(427,\cdot)\) \(\chi_{1328}(443,\cdot)\) \(\chi_{1328}(451,\cdot)\) \(\chi_{1328}(459,\cdot)\) \(\chi_{1328}(483,\cdot)\) \(\chi_{1328}(507,\cdot)\) \(\chi_{1328}(515,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{164})$ |
| Fixed field: | Number field defined by a degree 164 polynomial (not computed) |
Values on generators
\((831,997,417)\) → \((-1,i,e\left(\frac{19}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1328 }(363, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{164}\right)\) | \(e\left(\frac{125}{164}\right)\) | \(e\left(\frac{29}{41}\right)\) | \(e\left(\frac{19}{82}\right)\) | \(e\left(\frac{143}{164}\right)\) | \(e\left(\frac{71}{164}\right)\) | \(e\left(\frac{31}{82}\right)\) | \(e\left(\frac{39}{41}\right)\) | \(e\left(\frac{5}{164}\right)\) | \(e\left(\frac{53}{164}\right)\) |