Basic properties
Modulus: | \(768\) | |
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 \(\chi_{256}(115,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 768.bb
\(\chi_{768}(19,\cdot)\) \(\chi_{768}(43,\cdot)\) \(\chi_{768}(67,\cdot)\) \(\chi_{768}(91,\cdot)\) \(\chi_{768}(115,\cdot)\) \(\chi_{768}(139,\cdot)\) \(\chi_{768}(163,\cdot)\) \(\chi_{768}(187,\cdot)\) \(\chi_{768}(211,\cdot)\) \(\chi_{768}(235,\cdot)\) \(\chi_{768}(259,\cdot)\) \(\chi_{768}(283,\cdot)\) \(\chi_{768}(307,\cdot)\) \(\chi_{768}(331,\cdot)\) \(\chi_{768}(355,\cdot)\) \(\chi_{768}(379,\cdot)\) \(\chi_{768}(403,\cdot)\) \(\chi_{768}(427,\cdot)\) \(\chi_{768}(451,\cdot)\) \(\chi_{768}(475,\cdot)\) \(\chi_{768}(499,\cdot)\) \(\chi_{768}(523,\cdot)\) \(\chi_{768}(547,\cdot)\) \(\chi_{768}(571,\cdot)\) \(\chi_{768}(595,\cdot)\) \(\chi_{768}(619,\cdot)\) \(\chi_{768}(643,\cdot)\) \(\chi_{768}(667,\cdot)\) \(\chi_{768}(691,\cdot)\) \(\chi_{768}(715,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,517,257)\) → \((-1,e\left(\frac{15}{64}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 768 }(115, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |