Basic properties
Modulus: | \(731\) | |
Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(336\) | 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 731.bn
\(\chi_{731}(10,\cdot)\) \(\chi_{731}(14,\cdot)\) \(\chi_{731}(23,\cdot)\) \(\chi_{731}(24,\cdot)\) \(\chi_{731}(31,\cdot)\) \(\chi_{731}(40,\cdot)\) \(\chi_{731}(56,\cdot)\) \(\chi_{731}(57,\cdot)\) \(\chi_{731}(58,\cdot)\) \(\chi_{731}(74,\cdot)\) \(\chi_{731}(95,\cdot)\) \(\chi_{731}(96,\cdot)\) \(\chi_{731}(99,\cdot)\) \(\chi_{731}(109,\cdot)\) \(\chi_{731}(124,\cdot)\) \(\chi_{731}(126,\cdot)\) \(\chi_{731}(139,\cdot)\) \(\chi_{731}(142,\cdot)\) \(\chi_{731}(143,\cdot)\) \(\chi_{731}(146,\cdot)\) \(\chi_{731}(160,\cdot)\) \(\chi_{731}(167,\cdot)\) \(\chi_{731}(181,\cdot)\) \(\chi_{731}(182,\cdot)\) \(\chi_{731}(197,\cdot)\) \(\chi_{731}(210,\cdot)\) \(\chi_{731}(224,\cdot)\) \(\chi_{731}(228,\cdot)\) \(\chi_{731}(232,\cdot)\) \(\chi_{731}(267,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{336})$ |
Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((173,562)\) → \((e\left(\frac{15}{16}\right),e\left(\frac{8}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 731 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{107}{336}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{71}{336}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{107}{168}\right)\) | \(e\left(\frac{209}{336}\right)\) | \(e\left(\frac{111}{112}\right)\) |