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 \(\chi_{768}(251,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2304.bu
\(\chi_{2304}(35,\cdot)\) \(\chi_{2304}(107,\cdot)\) \(\chi_{2304}(179,\cdot)\) \(\chi_{2304}(251,\cdot)\) \(\chi_{2304}(323,\cdot)\) \(\chi_{2304}(395,\cdot)\) \(\chi_{2304}(467,\cdot)\) \(\chi_{2304}(539,\cdot)\) \(\chi_{2304}(611,\cdot)\) \(\chi_{2304}(683,\cdot)\) \(\chi_{2304}(755,\cdot)\) \(\chi_{2304}(827,\cdot)\) \(\chi_{2304}(899,\cdot)\) \(\chi_{2304}(971,\cdot)\) \(\chi_{2304}(1043,\cdot)\) \(\chi_{2304}(1115,\cdot)\) \(\chi_{2304}(1187,\cdot)\) \(\chi_{2304}(1259,\cdot)\) \(\chi_{2304}(1331,\cdot)\) \(\chi_{2304}(1403,\cdot)\) \(\chi_{2304}(1475,\cdot)\) \(\chi_{2304}(1547,\cdot)\) \(\chi_{2304}(1619,\cdot)\) \(\chi_{2304}(1691,\cdot)\) \(\chi_{2304}(1763,\cdot)\) \(\chi_{2304}(1835,\cdot)\) \(\chi_{2304}(1907,\cdot)\) \(\chi_{2304}(1979,\cdot)\) \(\chi_{2304}(2051,\cdot)\) \(\chi_{2304}(2123,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1279,2053,1793)\) → \((-1,e\left(\frac{1}{64}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2304 }(251, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |