Basic properties
| Modulus: | \(722\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 722.i
\(\chi_{722}(7,\cdot)\) \(\chi_{722}(11,\cdot)\) \(\chi_{722}(45,\cdot)\) \(\chi_{722}(49,\cdot)\) \(\chi_{722}(83,\cdot)\) \(\chi_{722}(87,\cdot)\) \(\chi_{722}(121,\cdot)\) \(\chi_{722}(125,\cdot)\) \(\chi_{722}(159,\cdot)\) \(\chi_{722}(163,\cdot)\) \(\chi_{722}(197,\cdot)\) \(\chi_{722}(201,\cdot)\) \(\chi_{722}(235,\cdot)\) \(\chi_{722}(239,\cdot)\) \(\chi_{722}(273,\cdot)\) \(\chi_{722}(277,\cdot)\) \(\chi_{722}(311,\cdot)\) \(\chi_{722}(315,\cdot)\) \(\chi_{722}(349,\cdot)\) \(\chi_{722}(353,\cdot)\) \(\chi_{722}(387,\cdot)\) \(\chi_{722}(391,\cdot)\) \(\chi_{722}(425,\cdot)\) \(\chi_{722}(463,\cdot)\) \(\chi_{722}(467,\cdot)\) \(\chi_{722}(501,\cdot)\) \(\chi_{722}(505,\cdot)\) \(\chi_{722}(539,\cdot)\) \(\chi_{722}(543,\cdot)\) \(\chi_{722}(577,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\(363\) → \(e\left(\frac{25}{57}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 722 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) |