Basic properties
Modulus: | \(1944\) | |
Conductor: | \(1944\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(162\) | 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 1944.bh
\(\chi_{1944}(43,\cdot)\) \(\chi_{1944}(67,\cdot)\) \(\chi_{1944}(115,\cdot)\) \(\chi_{1944}(139,\cdot)\) \(\chi_{1944}(187,\cdot)\) \(\chi_{1944}(211,\cdot)\) \(\chi_{1944}(259,\cdot)\) \(\chi_{1944}(283,\cdot)\) \(\chi_{1944}(331,\cdot)\) \(\chi_{1944}(355,\cdot)\) \(\chi_{1944}(403,\cdot)\) \(\chi_{1944}(427,\cdot)\) \(\chi_{1944}(475,\cdot)\) \(\chi_{1944}(499,\cdot)\) \(\chi_{1944}(547,\cdot)\) \(\chi_{1944}(571,\cdot)\) \(\chi_{1944}(619,\cdot)\) \(\chi_{1944}(643,\cdot)\) \(\chi_{1944}(691,\cdot)\) \(\chi_{1944}(715,\cdot)\) \(\chi_{1944}(763,\cdot)\) \(\chi_{1944}(787,\cdot)\) \(\chi_{1944}(835,\cdot)\) \(\chi_{1944}(859,\cdot)\) \(\chi_{1944}(907,\cdot)\) \(\chi_{1944}(931,\cdot)\) \(\chi_{1944}(979,\cdot)\) \(\chi_{1944}(1003,\cdot)\) \(\chi_{1944}(1051,\cdot)\) \(\chi_{1944}(1075,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{81})$ |
Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((487,973,1217)\) → \((-1,-1,e\left(\frac{61}{81}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1944 }(1723, a) \) | \(-1\) | \(1\) | \(e\left(\frac{133}{162}\right)\) | \(e\left(\frac{35}{162}\right)\) | \(e\left(\frac{10}{81}\right)\) | \(e\left(\frac{85}{162}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{73}{162}\right)\) | \(e\left(\frac{52}{81}\right)\) | \(e\left(\frac{59}{162}\right)\) | \(e\left(\frac{91}{162}\right)\) |