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.bn
\(\chi_{1944}(5,\cdot)\) \(\chi_{1944}(29,\cdot)\) \(\chi_{1944}(77,\cdot)\) \(\chi_{1944}(101,\cdot)\) \(\chi_{1944}(149,\cdot)\) \(\chi_{1944}(173,\cdot)\) \(\chi_{1944}(221,\cdot)\) \(\chi_{1944}(245,\cdot)\) \(\chi_{1944}(293,\cdot)\) \(\chi_{1944}(317,\cdot)\) \(\chi_{1944}(365,\cdot)\) \(\chi_{1944}(389,\cdot)\) \(\chi_{1944}(437,\cdot)\) \(\chi_{1944}(461,\cdot)\) \(\chi_{1944}(509,\cdot)\) \(\chi_{1944}(533,\cdot)\) \(\chi_{1944}(581,\cdot)\) \(\chi_{1944}(605,\cdot)\) \(\chi_{1944}(653,\cdot)\) \(\chi_{1944}(677,\cdot)\) \(\chi_{1944}(725,\cdot)\) \(\chi_{1944}(749,\cdot)\) \(\chi_{1944}(797,\cdot)\) \(\chi_{1944}(821,\cdot)\) \(\chi_{1944}(869,\cdot)\) \(\chi_{1944}(893,\cdot)\) \(\chi_{1944}(941,\cdot)\) \(\chi_{1944}(965,\cdot)\) \(\chi_{1944}(1013,\cdot)\) \(\chi_{1944}(1037,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{81})$ |
Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((487,973,1217)\) → \((1,-1,e\left(\frac{83}{162}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1944 }(725, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{81}\right)\) | \(e\left(\frac{70}{81}\right)\) | \(e\left(\frac{40}{81}\right)\) | \(e\left(\frac{97}{162}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{49}{162}\right)\) | \(e\left(\frac{46}{81}\right)\) | \(e\left(\frac{37}{81}\right)\) | \(e\left(\frac{20}{81}\right)\) |