Basic properties
Modulus: | \(731\) | |
Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(168\) | 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 731.bl
\(\chi_{731}(9,\cdot)\) \(\chi_{731}(15,\cdot)\) \(\chi_{731}(25,\cdot)\) \(\chi_{731}(53,\cdot)\) \(\chi_{731}(60,\cdot)\) \(\chi_{731}(66,\cdot)\) \(\chi_{731}(83,\cdot)\) \(\chi_{731}(100,\cdot)\) \(\chi_{731}(110,\cdot)\) \(\chi_{731}(111,\cdot)\) \(\chi_{731}(117,\cdot)\) \(\chi_{731}(138,\cdot)\) \(\chi_{731}(144,\cdot)\) \(\chi_{731}(185,\cdot)\) \(\chi_{731}(189,\cdot)\) \(\chi_{731}(195,\cdot)\) \(\chi_{731}(196,\cdot)\) \(\chi_{731}(212,\cdot)\) \(\chi_{731}(229,\cdot)\) \(\chi_{731}(230,\cdot)\) \(\chi_{731}(240,\cdot)\) \(\chi_{731}(246,\cdot)\) \(\chi_{731}(253,\cdot)\) \(\chi_{731}(281,\cdot)\) \(\chi_{731}(298,\cdot)\) \(\chi_{731}(314,\cdot)\) \(\chi_{731}(315,\cdot)\) \(\chi_{731}(325,\cdot)\) \(\chi_{731}(332,\cdot)\) \(\chi_{731}(359,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{168})$ |
Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((173,562)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{20}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 731 }(325, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{139}{168}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{31}{168}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{25}{168}\right)\) | \(e\left(\frac{39}{56}\right)\) |