Basic properties
Modulus: | \(3328\) | |
Conductor: | \(3328\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | 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 3328.dh
\(\chi_{3328}(51,\cdot)\) \(\chi_{3328}(155,\cdot)\) \(\chi_{3328}(259,\cdot)\) \(\chi_{3328}(363,\cdot)\) \(\chi_{3328}(467,\cdot)\) \(\chi_{3328}(571,\cdot)\) \(\chi_{3328}(675,\cdot)\) \(\chi_{3328}(779,\cdot)\) \(\chi_{3328}(883,\cdot)\) \(\chi_{3328}(987,\cdot)\) \(\chi_{3328}(1091,\cdot)\) \(\chi_{3328}(1195,\cdot)\) \(\chi_{3328}(1299,\cdot)\) \(\chi_{3328}(1403,\cdot)\) \(\chi_{3328}(1507,\cdot)\) \(\chi_{3328}(1611,\cdot)\) \(\chi_{3328}(1715,\cdot)\) \(\chi_{3328}(1819,\cdot)\) \(\chi_{3328}(1923,\cdot)\) \(\chi_{3328}(2027,\cdot)\) \(\chi_{3328}(2131,\cdot)\) \(\chi_{3328}(2235,\cdot)\) \(\chi_{3328}(2339,\cdot)\) \(\chi_{3328}(2443,\cdot)\) \(\chi_{3328}(2547,\cdot)\) \(\chi_{3328}(2651,\cdot)\) \(\chi_{3328}(2755,\cdot)\) \(\chi_{3328}(2859,\cdot)\) \(\chi_{3328}(2963,\cdot)\) \(\chi_{3328}(3067,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1535,261,769)\) → \((-1,e\left(\frac{63}{64}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 3328 }(51, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{9}{32}\right)\) |