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
\((831,997,417)\) → \((-1,-i,e\left(\frac{3}{41}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1328 }(147, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{164}\right)\) | \(e\left(\frac{119}{164}\right)\) | \(e\left(\frac{24}{41}\right)\) | \(e\left(\frac{3}{82}\right)\) | \(e\left(\frac{1}{164}\right)\) | \(e\left(\frac{145}{164}\right)\) | \(e\left(\frac{61}{82}\right)\) | \(e\left(\frac{4}{41}\right)\) | \(e\left(\frac{31}{164}\right)\) | \(e\left(\frac{99}{164}\right)\) |