Basic properties
| Modulus: | \(1681\) | |
| Conductor: | \(1681\) | 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 1681.k
\(\chi_{1681}(9,\cdot)\) \(\chi_{1681}(32,\cdot)\) \(\chi_{1681}(50,\cdot)\) \(\chi_{1681}(73,\cdot)\) \(\chi_{1681}(91,\cdot)\) \(\chi_{1681}(114,\cdot)\) \(\chi_{1681}(132,\cdot)\) \(\chi_{1681}(155,\cdot)\) \(\chi_{1681}(173,\cdot)\) \(\chi_{1681}(196,\cdot)\) \(\chi_{1681}(214,\cdot)\) \(\chi_{1681}(237,\cdot)\) \(\chi_{1681}(255,\cdot)\) \(\chi_{1681}(278,\cdot)\) \(\chi_{1681}(296,\cdot)\) \(\chi_{1681}(319,\cdot)\) \(\chi_{1681}(337,\cdot)\) \(\chi_{1681}(360,\cdot)\) \(\chi_{1681}(401,\cdot)\) \(\chi_{1681}(419,\cdot)\) \(\chi_{1681}(442,\cdot)\) \(\chi_{1681}(460,\cdot)\) \(\chi_{1681}(483,\cdot)\) \(\chi_{1681}(501,\cdot)\) \(\chi_{1681}(524,\cdot)\) \(\chi_{1681}(542,\cdot)\) \(\chi_{1681}(565,\cdot)\) \(\chi_{1681}(583,\cdot)\) \(\chi_{1681}(606,\cdot)\) \(\chi_{1681}(624,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{164})$ |
| Fixed field: | Number field defined by a degree 164 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{153}{164}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1681 }(565, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{82}\right)\) | \(e\left(\frac{87}{164}\right)\) | \(e\left(\frac{33}{41}\right)\) | \(e\left(\frac{29}{82}\right)\) | \(e\left(\frac{153}{164}\right)\) | \(e\left(\frac{83}{164}\right)\) | \(e\left(\frac{17}{82}\right)\) | \(e\left(\frac{5}{82}\right)\) | \(e\left(\frac{31}{41}\right)\) | \(e\left(\frac{143}{164}\right)\) |