Basic properties
| Modulus: | \(3888\) | |
| Conductor: | \(1296\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1296}(637,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3888.bw
\(\chi_{3888}(37,\cdot)\) \(\chi_{3888}(181,\cdot)\) \(\chi_{3888}(253,\cdot)\) \(\chi_{3888}(397,\cdot)\) \(\chi_{3888}(469,\cdot)\) \(\chi_{3888}(613,\cdot)\) \(\chi_{3888}(685,\cdot)\) \(\chi_{3888}(829,\cdot)\) \(\chi_{3888}(901,\cdot)\) \(\chi_{3888}(1045,\cdot)\) \(\chi_{3888}(1117,\cdot)\) \(\chi_{3888}(1261,\cdot)\) \(\chi_{3888}(1333,\cdot)\) \(\chi_{3888}(1477,\cdot)\) \(\chi_{3888}(1549,\cdot)\) \(\chi_{3888}(1693,\cdot)\) \(\chi_{3888}(1765,\cdot)\) \(\chi_{3888}(1909,\cdot)\) \(\chi_{3888}(1981,\cdot)\) \(\chi_{3888}(2125,\cdot)\) \(\chi_{3888}(2197,\cdot)\) \(\chi_{3888}(2341,\cdot)\) \(\chi_{3888}(2413,\cdot)\) \(\chi_{3888}(2557,\cdot)\) \(\chi_{3888}(2629,\cdot)\) \(\chi_{3888}(2773,\cdot)\) \(\chi_{3888}(2845,\cdot)\) \(\chi_{3888}(2989,\cdot)\) \(\chi_{3888}(3061,\cdot)\) \(\chi_{3888}(3205,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,2917,1217)\) → \((1,-i,e\left(\frac{20}{27}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3888 }(2557, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{108}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{19}{108}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{22}{27}\right)\) |