Basic properties
| Modulus: | \(1944\) | |
| Conductor: | \(243\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(162\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{243}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1944.bk
\(\chi_{1944}(41,\cdot)\) \(\chi_{1944}(65,\cdot)\) \(\chi_{1944}(113,\cdot)\) \(\chi_{1944}(137,\cdot)\) \(\chi_{1944}(185,\cdot)\) \(\chi_{1944}(209,\cdot)\) \(\chi_{1944}(257,\cdot)\) \(\chi_{1944}(281,\cdot)\) \(\chi_{1944}(329,\cdot)\) \(\chi_{1944}(353,\cdot)\) \(\chi_{1944}(401,\cdot)\) \(\chi_{1944}(425,\cdot)\) \(\chi_{1944}(473,\cdot)\) \(\chi_{1944}(497,\cdot)\) \(\chi_{1944}(545,\cdot)\) \(\chi_{1944}(569,\cdot)\) \(\chi_{1944}(617,\cdot)\) \(\chi_{1944}(641,\cdot)\) \(\chi_{1944}(689,\cdot)\) \(\chi_{1944}(713,\cdot)\) \(\chi_{1944}(761,\cdot)\) \(\chi_{1944}(785,\cdot)\) \(\chi_{1944}(833,\cdot)\) \(\chi_{1944}(857,\cdot)\) \(\chi_{1944}(905,\cdot)\) \(\chi_{1944}(929,\cdot)\) \(\chi_{1944}(977,\cdot)\) \(\chi_{1944}(1001,\cdot)\) \(\chi_{1944}(1049,\cdot)\) \(\chi_{1944}(1073,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((487,973,1217)\) → \((1,1,e\left(\frac{53}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1944 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{85}{162}\right)\) | \(e\left(\frac{73}{81}\right)\) | \(e\left(\frac{95}{162}\right)\) | \(e\left(\frac{50}{81}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{43}{162}\right)\) | \(e\left(\frac{4}{81}\right)\) | \(e\left(\frac{17}{162}\right)\) | \(e\left(\frac{44}{81}\right)\) |