Basic properties
| Modulus: | \(768\) | |
| 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 \(\chi_{256}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 768.z
\(\chi_{768}(13,\cdot)\) \(\chi_{768}(37,\cdot)\) \(\chi_{768}(61,\cdot)\) \(\chi_{768}(85,\cdot)\) \(\chi_{768}(109,\cdot)\) \(\chi_{768}(133,\cdot)\) \(\chi_{768}(157,\cdot)\) \(\chi_{768}(181,\cdot)\) \(\chi_{768}(205,\cdot)\) \(\chi_{768}(229,\cdot)\) \(\chi_{768}(253,\cdot)\) \(\chi_{768}(277,\cdot)\) \(\chi_{768}(301,\cdot)\) \(\chi_{768}(325,\cdot)\) \(\chi_{768}(349,\cdot)\) \(\chi_{768}(373,\cdot)\) \(\chi_{768}(397,\cdot)\) \(\chi_{768}(421,\cdot)\) \(\chi_{768}(445,\cdot)\) \(\chi_{768}(469,\cdot)\) \(\chi_{768}(493,\cdot)\) \(\chi_{768}(517,\cdot)\) \(\chi_{768}(541,\cdot)\) \(\chi_{768}(565,\cdot)\) \(\chi_{768}(589,\cdot)\) \(\chi_{768}(613,\cdot)\) \(\chi_{768}(637,\cdot)\) \(\chi_{768}(661,\cdot)\) \(\chi_{768}(685,\cdot)\) \(\chi_{768}(709,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,517,257)\) → \((1,e\left(\frac{19}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 768 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |