Basic properties
| Modulus: | \(1792\) | |
| 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 \(\chi_{256}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1792.bu
\(\chi_{1792}(43,\cdot)\) \(\chi_{1792}(99,\cdot)\) \(\chi_{1792}(155,\cdot)\) \(\chi_{1792}(211,\cdot)\) \(\chi_{1792}(267,\cdot)\) \(\chi_{1792}(323,\cdot)\) \(\chi_{1792}(379,\cdot)\) \(\chi_{1792}(435,\cdot)\) \(\chi_{1792}(491,\cdot)\) \(\chi_{1792}(547,\cdot)\) \(\chi_{1792}(603,\cdot)\) \(\chi_{1792}(659,\cdot)\) \(\chi_{1792}(715,\cdot)\) \(\chi_{1792}(771,\cdot)\) \(\chi_{1792}(827,\cdot)\) \(\chi_{1792}(883,\cdot)\) \(\chi_{1792}(939,\cdot)\) \(\chi_{1792}(995,\cdot)\) \(\chi_{1792}(1051,\cdot)\) \(\chi_{1792}(1107,\cdot)\) \(\chi_{1792}(1163,\cdot)\) \(\chi_{1792}(1219,\cdot)\) \(\chi_{1792}(1275,\cdot)\) \(\chi_{1792}(1331,\cdot)\) \(\chi_{1792}(1387,\cdot)\) \(\chi_{1792}(1443,\cdot)\) \(\chi_{1792}(1499,\cdot)\) \(\chi_{1792}(1555,\cdot)\) \(\chi_{1792}(1611,\cdot)\) \(\chi_{1792}(1667,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{61}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1792 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) |