Basic properties
| Modulus: | \(3328\) | |
| Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{256}(27,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3328.dg
\(\chi_{3328}(27,\cdot)\) \(\chi_{3328}(131,\cdot)\) \(\chi_{3328}(235,\cdot)\) \(\chi_{3328}(339,\cdot)\) \(\chi_{3328}(443,\cdot)\) \(\chi_{3328}(547,\cdot)\) \(\chi_{3328}(651,\cdot)\) \(\chi_{3328}(755,\cdot)\) \(\chi_{3328}(859,\cdot)\) \(\chi_{3328}(963,\cdot)\) \(\chi_{3328}(1067,\cdot)\) \(\chi_{3328}(1171,\cdot)\) \(\chi_{3328}(1275,\cdot)\) \(\chi_{3328}(1379,\cdot)\) \(\chi_{3328}(1483,\cdot)\) \(\chi_{3328}(1587,\cdot)\) \(\chi_{3328}(1691,\cdot)\) \(\chi_{3328}(1795,\cdot)\) \(\chi_{3328}(1899,\cdot)\) \(\chi_{3328}(2003,\cdot)\) \(\chi_{3328}(2107,\cdot)\) \(\chi_{3328}(2211,\cdot)\) \(\chi_{3328}(2315,\cdot)\) \(\chi_{3328}(2419,\cdot)\) \(\chi_{3328}(2523,\cdot)\) \(\chi_{3328}(2627,\cdot)\) \(\chi_{3328}(2731,\cdot)\) \(\chi_{3328}(2835,\cdot)\) \(\chi_{3328}(2939,\cdot)\) \(\chi_{3328}(3043,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1535,261,769)\) → \((-1,e\left(\frac{41}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3328 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{15}{32}\right)\) |