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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1328.u
\(\chi_{1328}(19,\cdot)\) \(\chi_{1328}(35,\cdot)\) \(\chi_{1328}(43,\cdot)\) \(\chi_{1328}(67,\cdot)\) \(\chi_{1328}(91,\cdot)\) \(\chi_{1328}(107,\cdot)\) \(\chi_{1328}(115,\cdot)\) \(\chi_{1328}(139,\cdot)\) \(\chi_{1328}(155,\cdot)\) \(\chi_{1328}(163,\cdot)\) \(\chi_{1328}(171,\cdot)\) \(\chi_{1328}(179,\cdot)\) \(\chi_{1328}(211,\cdot)\) \(\chi_{1328}(219,\cdot)\) \(\chi_{1328}(251,\cdot)\) \(\chi_{1328}(267,\cdot)\) \(\chi_{1328}(283,\cdot)\) \(\chi_{1328}(291,\cdot)\) \(\chi_{1328}(299,\cdot)\) \(\chi_{1328}(307,\cdot)\) \(\chi_{1328}(315,\cdot)\) \(\chi_{1328}(323,\cdot)\) \(\chi_{1328}(347,\cdot)\) \(\chi_{1328}(371,\cdot)\) \(\chi_{1328}(379,\cdot)\) \(\chi_{1328}(387,\cdot)\) \(\chi_{1328}(403,\cdot)\) \(\chi_{1328}(411,\cdot)\) \(\chi_{1328}(435,\cdot)\) \(\chi_{1328}(467,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{164})$ |
Fixed field: | Number field defined by a degree 164 polynomial (not computed) |
Values on generators
\((831,997,417)\) → \((-1,-i,e\left(\frac{79}{82}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1328 }(467, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{164}\right)\) | \(e\left(\frac{125}{164}\right)\) | \(e\left(\frac{29}{41}\right)\) | \(e\left(\frac{19}{82}\right)\) | \(e\left(\frac{61}{164}\right)\) | \(e\left(\frac{71}{164}\right)\) | \(e\left(\frac{36}{41}\right)\) | \(e\left(\frac{39}{41}\right)\) | \(e\left(\frac{5}{164}\right)\) | \(e\left(\frac{135}{164}\right)\) |