Basic properties
Modulus: | \(2304\) | |
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 \(\chi_{256}(227,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.bv
\(\chi_{2304}(19,\cdot)\) \(\chi_{2304}(91,\cdot)\) \(\chi_{2304}(163,\cdot)\) \(\chi_{2304}(235,\cdot)\) \(\chi_{2304}(307,\cdot)\) \(\chi_{2304}(379,\cdot)\) \(\chi_{2304}(451,\cdot)\) \(\chi_{2304}(523,\cdot)\) \(\chi_{2304}(595,\cdot)\) \(\chi_{2304}(667,\cdot)\) \(\chi_{2304}(739,\cdot)\) \(\chi_{2304}(811,\cdot)\) \(\chi_{2304}(883,\cdot)\) \(\chi_{2304}(955,\cdot)\) \(\chi_{2304}(1027,\cdot)\) \(\chi_{2304}(1099,\cdot)\) \(\chi_{2304}(1171,\cdot)\) \(\chi_{2304}(1243,\cdot)\) \(\chi_{2304}(1315,\cdot)\) \(\chi_{2304}(1387,\cdot)\) \(\chi_{2304}(1459,\cdot)\) \(\chi_{2304}(1531,\cdot)\) \(\chi_{2304}(1603,\cdot)\) \(\chi_{2304}(1675,\cdot)\) \(\chi_{2304}(1747,\cdot)\) \(\chi_{2304}(1819,\cdot)\) \(\chi_{2304}(1891,\cdot)\) \(\chi_{2304}(1963,\cdot)\) \(\chi_{2304}(2035,\cdot)\) \(\chi_{2304}(2107,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1279,2053,1793)\) → \((-1,e\left(\frac{59}{64}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2304 }(739, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |