Basic properties
Modulus: | \(2304\) | |
Conductor: | \(768\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{768}(317,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.bs
\(\chi_{2304}(53,\cdot)\) \(\chi_{2304}(125,\cdot)\) \(\chi_{2304}(197,\cdot)\) \(\chi_{2304}(269,\cdot)\) \(\chi_{2304}(341,\cdot)\) \(\chi_{2304}(413,\cdot)\) \(\chi_{2304}(485,\cdot)\) \(\chi_{2304}(557,\cdot)\) \(\chi_{2304}(629,\cdot)\) \(\chi_{2304}(701,\cdot)\) \(\chi_{2304}(773,\cdot)\) \(\chi_{2304}(845,\cdot)\) \(\chi_{2304}(917,\cdot)\) \(\chi_{2304}(989,\cdot)\) \(\chi_{2304}(1061,\cdot)\) \(\chi_{2304}(1133,\cdot)\) \(\chi_{2304}(1205,\cdot)\) \(\chi_{2304}(1277,\cdot)\) \(\chi_{2304}(1349,\cdot)\) \(\chi_{2304}(1421,\cdot)\) \(\chi_{2304}(1493,\cdot)\) \(\chi_{2304}(1565,\cdot)\) \(\chi_{2304}(1637,\cdot)\) \(\chi_{2304}(1709,\cdot)\) \(\chi_{2304}(1781,\cdot)\) \(\chi_{2304}(1853,\cdot)\) \(\chi_{2304}(1925,\cdot)\) \(\chi_{2304}(1997,\cdot)\) \(\chi_{2304}(2069,\cdot)\) \(\chi_{2304}(2141,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1279,2053,1793)\) → \((1,e\left(\frac{19}{64}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 2304 }(1853, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |