Basic properties
Modulus: | \(1944\) | |
Conductor: | \(972\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(162\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{972}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1944.bi
\(\chi_{1944}(7,\cdot)\) \(\chi_{1944}(31,\cdot)\) \(\chi_{1944}(79,\cdot)\) \(\chi_{1944}(103,\cdot)\) \(\chi_{1944}(151,\cdot)\) \(\chi_{1944}(175,\cdot)\) \(\chi_{1944}(223,\cdot)\) \(\chi_{1944}(247,\cdot)\) \(\chi_{1944}(295,\cdot)\) \(\chi_{1944}(319,\cdot)\) \(\chi_{1944}(367,\cdot)\) \(\chi_{1944}(391,\cdot)\) \(\chi_{1944}(439,\cdot)\) \(\chi_{1944}(463,\cdot)\) \(\chi_{1944}(511,\cdot)\) \(\chi_{1944}(535,\cdot)\) \(\chi_{1944}(583,\cdot)\) \(\chi_{1944}(607,\cdot)\) \(\chi_{1944}(655,\cdot)\) \(\chi_{1944}(679,\cdot)\) \(\chi_{1944}(727,\cdot)\) \(\chi_{1944}(751,\cdot)\) \(\chi_{1944}(799,\cdot)\) \(\chi_{1944}(823,\cdot)\) \(\chi_{1944}(871,\cdot)\) \(\chi_{1944}(895,\cdot)\) \(\chi_{1944}(943,\cdot)\) \(\chi_{1944}(967,\cdot)\) \(\chi_{1944}(1015,\cdot)\) \(\chi_{1944}(1039,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{81})$ |
Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((487,973,1217)\) → \((-1,1,e\left(\frac{68}{81}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1944 }(79, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{81}\right)\) | \(e\left(\frac{43}{162}\right)\) | \(e\left(\frac{13}{162}\right)\) | \(e\left(\frac{58}{81}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{11}{162}\right)\) | \(e\left(\frac{50}{81}\right)\) | \(e\left(\frac{5}{81}\right)\) | \(e\left(\frac{47}{162}\right)\) |