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 \(\chi_{1296}(475,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3888.bu
\(\chi_{3888}(19,\cdot)\) \(\chi_{3888}(91,\cdot)\) \(\chi_{3888}(235,\cdot)\) \(\chi_{3888}(307,\cdot)\) \(\chi_{3888}(451,\cdot)\) \(\chi_{3888}(523,\cdot)\) \(\chi_{3888}(667,\cdot)\) \(\chi_{3888}(739,\cdot)\) \(\chi_{3888}(883,\cdot)\) \(\chi_{3888}(955,\cdot)\) \(\chi_{3888}(1099,\cdot)\) \(\chi_{3888}(1171,\cdot)\) \(\chi_{3888}(1315,\cdot)\) \(\chi_{3888}(1387,\cdot)\) \(\chi_{3888}(1531,\cdot)\) \(\chi_{3888}(1603,\cdot)\) \(\chi_{3888}(1747,\cdot)\) \(\chi_{3888}(1819,\cdot)\) \(\chi_{3888}(1963,\cdot)\) \(\chi_{3888}(2035,\cdot)\) \(\chi_{3888}(2179,\cdot)\) \(\chi_{3888}(2251,\cdot)\) \(\chi_{3888}(2395,\cdot)\) \(\chi_{3888}(2467,\cdot)\) \(\chi_{3888}(2611,\cdot)\) \(\chi_{3888}(2683,\cdot)\) \(\chi_{3888}(2827,\cdot)\) \(\chi_{3888}(2899,\cdot)\) \(\chi_{3888}(3043,\cdot)\) \(\chi_{3888}(3115,\cdot)\) ...
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
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3888 }(1099, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{108}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{17}{54}\right)\) |