Basic properties
Modulus: | \(731\) | |
Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | 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.bf
\(\chi_{731}(2,\cdot)\) \(\chi_{731}(8,\cdot)\) \(\chi_{731}(32,\cdot)\) \(\chi_{731}(70,\cdot)\) \(\chi_{731}(94,\cdot)\) \(\chi_{731}(151,\cdot)\) \(\chi_{731}(161,\cdot)\) \(\chi_{731}(168,\cdot)\) \(\chi_{731}(223,\cdot)\) \(\chi_{731}(247,\cdot)\) \(\chi_{731}(280,\cdot)\) \(\chi_{731}(297,\cdot)\) \(\chi_{731}(366,\cdot)\) \(\chi_{731}(376,\cdot)\) \(\chi_{731}(383,\cdot)\) \(\chi_{731}(389,\cdot)\) \(\chi_{731}(457,\cdot)\) \(\chi_{731}(495,\cdot)\) \(\chi_{731}(512,\cdot)\) \(\chi_{731}(518,\cdot)\) \(\chi_{731}(586,\cdot)\) \(\chi_{731}(604,\cdot)\) \(\chi_{731}(610,\cdot)\) \(\chi_{731}(672,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((173,562)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{9}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 731 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{25}{56}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{23}{56}\right)\) |