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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 768.ba
\(\chi_{768}(11,\cdot)\) \(\chi_{768}(35,\cdot)\) \(\chi_{768}(59,\cdot)\) \(\chi_{768}(83,\cdot)\) \(\chi_{768}(107,\cdot)\) \(\chi_{768}(131,\cdot)\) \(\chi_{768}(155,\cdot)\) \(\chi_{768}(179,\cdot)\) \(\chi_{768}(203,\cdot)\) \(\chi_{768}(227,\cdot)\) \(\chi_{768}(251,\cdot)\) \(\chi_{768}(275,\cdot)\) \(\chi_{768}(299,\cdot)\) \(\chi_{768}(323,\cdot)\) \(\chi_{768}(347,\cdot)\) \(\chi_{768}(371,\cdot)\) \(\chi_{768}(395,\cdot)\) \(\chi_{768}(419,\cdot)\) \(\chi_{768}(443,\cdot)\) \(\chi_{768}(467,\cdot)\) \(\chi_{768}(491,\cdot)\) \(\chi_{768}(515,\cdot)\) \(\chi_{768}(539,\cdot)\) \(\chi_{768}(563,\cdot)\) \(\chi_{768}(587,\cdot)\) \(\chi_{768}(611,\cdot)\) \(\chi_{768}(635,\cdot)\) \(\chi_{768}(659,\cdot)\) \(\chi_{768}(683,\cdot)\) \(\chi_{768}(707,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,517,257)\) → \((-1,e\left(\frac{17}{64}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 768 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |