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 \(\chi_{256}(93,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.bt
\(\chi_{2304}(37,\cdot)\) \(\chi_{2304}(109,\cdot)\) \(\chi_{2304}(181,\cdot)\) \(\chi_{2304}(253,\cdot)\) \(\chi_{2304}(325,\cdot)\) \(\chi_{2304}(397,\cdot)\) \(\chi_{2304}(469,\cdot)\) \(\chi_{2304}(541,\cdot)\) \(\chi_{2304}(613,\cdot)\) \(\chi_{2304}(685,\cdot)\) \(\chi_{2304}(757,\cdot)\) \(\chi_{2304}(829,\cdot)\) \(\chi_{2304}(901,\cdot)\) \(\chi_{2304}(973,\cdot)\) \(\chi_{2304}(1045,\cdot)\) \(\chi_{2304}(1117,\cdot)\) \(\chi_{2304}(1189,\cdot)\) \(\chi_{2304}(1261,\cdot)\) \(\chi_{2304}(1333,\cdot)\) \(\chi_{2304}(1405,\cdot)\) \(\chi_{2304}(1477,\cdot)\) \(\chi_{2304}(1549,\cdot)\) \(\chi_{2304}(1621,\cdot)\) \(\chi_{2304}(1693,\cdot)\) \(\chi_{2304}(1765,\cdot)\) \(\chi_{2304}(1837,\cdot)\) \(\chi_{2304}(1909,\cdot)\) \(\chi_{2304}(1981,\cdot)\) \(\chi_{2304}(2053,\cdot)\) \(\chi_{2304}(2125,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1279,2053,1793)\) → \((1,e\left(\frac{43}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2304 }(1117, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |