Basic properties
Modulus: | \(659\) | |
Conductor: | \(659\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(47\) | 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 659.e
\(\chi_{659}(14,\cdot)\) \(\chi_{659}(15,\cdot)\) \(\chi_{659}(44,\cdot)\) \(\chi_{659}(57,\cdot)\) \(\chi_{659}(73,\cdot)\) \(\chi_{659}(80,\cdot)\) \(\chi_{659}(85,\cdot)\) \(\chi_{659}(108,\cdot)\) \(\chi_{659}(139,\cdot)\) \(\chi_{659}(156,\cdot)\) \(\chi_{659}(173,\cdot)\) \(\chi_{659}(185,\cdot)\) \(\chi_{659}(194,\cdot)\) \(\chi_{659}(196,\cdot)\) \(\chi_{659}(207,\cdot)\) \(\chi_{659}(210,\cdot)\) \(\chi_{659}(225,\cdot)\) \(\chi_{659}(232,\cdot)\) \(\chi_{659}(262,\cdot)\) \(\chi_{659}(274,\cdot)\) \(\chi_{659}(299,\cdot)\) \(\chi_{659}(302,\cdot)\) \(\chi_{659}(304,\cdot)\) \(\chi_{659}(323,\cdot)\) \(\chi_{659}(325,\cdot)\) \(\chi_{659}(363,\cdot)\) \(\chi_{659}(373,\cdot)\) \(\chi_{659}(436,\cdot)\) \(\chi_{659}(445,\cdot)\) \(\chi_{659}(461,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{47})$ |
Fixed field: | Number field defined by a degree 47 polynomial |
Values on generators
\(2\) → \(e\left(\frac{22}{47}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 659 }(194, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{47}\right)\) | \(e\left(\frac{3}{47}\right)\) | \(e\left(\frac{44}{47}\right)\) | \(e\left(\frac{16}{47}\right)\) | \(e\left(\frac{25}{47}\right)\) | \(e\left(\frac{27}{47}\right)\) | \(e\left(\frac{19}{47}\right)\) | \(e\left(\frac{6}{47}\right)\) | \(e\left(\frac{38}{47}\right)\) | \(e\left(\frac{31}{47}\right)\) |