Basic properties
Modulus: | \(768\) | |
Conductor: | \(768\) | 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 768.y
\(\chi_{768}(5,\cdot)\) \(\chi_{768}(29,\cdot)\) \(\chi_{768}(53,\cdot)\) \(\chi_{768}(77,\cdot)\) \(\chi_{768}(101,\cdot)\) \(\chi_{768}(125,\cdot)\) \(\chi_{768}(149,\cdot)\) \(\chi_{768}(173,\cdot)\) \(\chi_{768}(197,\cdot)\) \(\chi_{768}(221,\cdot)\) \(\chi_{768}(245,\cdot)\) \(\chi_{768}(269,\cdot)\) \(\chi_{768}(293,\cdot)\) \(\chi_{768}(317,\cdot)\) \(\chi_{768}(341,\cdot)\) \(\chi_{768}(365,\cdot)\) \(\chi_{768}(389,\cdot)\) \(\chi_{768}(413,\cdot)\) \(\chi_{768}(437,\cdot)\) \(\chi_{768}(461,\cdot)\) \(\chi_{768}(485,\cdot)\) \(\chi_{768}(509,\cdot)\) \(\chi_{768}(533,\cdot)\) \(\chi_{768}(557,\cdot)\) \(\chi_{768}(581,\cdot)\) \(\chi_{768}(605,\cdot)\) \(\chi_{768}(629,\cdot)\) \(\chi_{768}(653,\cdot)\) \(\chi_{768}(677,\cdot)\) \(\chi_{768}(701,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,517,257)\) → \((1,e\left(\frac{47}{64}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 768 }(269, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |