Basic properties
| Modulus: | \(3888\) | |
| Conductor: | \(1944\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(162\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1944}(1181,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3888.cd
\(\chi_{3888}(41,\cdot)\) \(\chi_{3888}(137,\cdot)\) \(\chi_{3888}(185,\cdot)\) \(\chi_{3888}(281,\cdot)\) \(\chi_{3888}(329,\cdot)\) \(\chi_{3888}(425,\cdot)\) \(\chi_{3888}(473,\cdot)\) \(\chi_{3888}(569,\cdot)\) \(\chi_{3888}(617,\cdot)\) \(\chi_{3888}(713,\cdot)\) \(\chi_{3888}(761,\cdot)\) \(\chi_{3888}(857,\cdot)\) \(\chi_{3888}(905,\cdot)\) \(\chi_{3888}(1001,\cdot)\) \(\chi_{3888}(1049,\cdot)\) \(\chi_{3888}(1145,\cdot)\) \(\chi_{3888}(1193,\cdot)\) \(\chi_{3888}(1289,\cdot)\) \(\chi_{3888}(1337,\cdot)\) \(\chi_{3888}(1433,\cdot)\) \(\chi_{3888}(1481,\cdot)\) \(\chi_{3888}(1577,\cdot)\) \(\chi_{3888}(1625,\cdot)\) \(\chi_{3888}(1721,\cdot)\) \(\chi_{3888}(1769,\cdot)\) \(\chi_{3888}(1865,\cdot)\) \(\chi_{3888}(1913,\cdot)\) \(\chi_{3888}(2009,\cdot)\) \(\chi_{3888}(2057,\cdot)\) \(\chi_{3888}(2153,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((2431,2917,1217)\) → \((1,-1,e\left(\frac{115}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3888 }(2153, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{81}\right)\) | \(e\left(\frac{56}{81}\right)\) | \(e\left(\frac{32}{81}\right)\) | \(e\left(\frac{29}{162}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{23}{162}\right)\) | \(e\left(\frac{53}{81}\right)\) | \(e\left(\frac{62}{81}\right)\) | \(e\left(\frac{16}{81}\right)\) |