Basic properties
| Modulus: | \(1444\) | |
| 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 \(\chi_{361}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1444.q
\(\chi_{1444}(45,\cdot)\) \(\chi_{1444}(49,\cdot)\) \(\chi_{1444}(121,\cdot)\) \(\chi_{1444}(125,\cdot)\) \(\chi_{1444}(197,\cdot)\) \(\chi_{1444}(201,\cdot)\) \(\chi_{1444}(273,\cdot)\) \(\chi_{1444}(277,\cdot)\) \(\chi_{1444}(349,\cdot)\) \(\chi_{1444}(353,\cdot)\) \(\chi_{1444}(425,\cdot)\) \(\chi_{1444}(501,\cdot)\) \(\chi_{1444}(505,\cdot)\) \(\chi_{1444}(577,\cdot)\) \(\chi_{1444}(581,\cdot)\) \(\chi_{1444}(657,\cdot)\) \(\chi_{1444}(729,\cdot)\) \(\chi_{1444}(733,\cdot)\) \(\chi_{1444}(805,\cdot)\) \(\chi_{1444}(809,\cdot)\) \(\chi_{1444}(881,\cdot)\) \(\chi_{1444}(885,\cdot)\) \(\chi_{1444}(957,\cdot)\) \(\chi_{1444}(961,\cdot)\) \(\chi_{1444}(1033,\cdot)\) \(\chi_{1444}(1037,\cdot)\) \(\chi_{1444}(1109,\cdot)\) \(\chi_{1444}(1113,\cdot)\) \(\chi_{1444}(1185,\cdot)\) \(\chi_{1444}(1189,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((723,1085)\) → \((1,e\left(\frac{28}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1444 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) |