Basic properties
| Modulus: | \(5376\) | |
| 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 \(\chi_{768}(155,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5376.dp
\(\chi_{5376}(155,\cdot)\) \(\chi_{5376}(323,\cdot)\) \(\chi_{5376}(491,\cdot)\) \(\chi_{5376}(659,\cdot)\) \(\chi_{5376}(827,\cdot)\) \(\chi_{5376}(995,\cdot)\) \(\chi_{5376}(1163,\cdot)\) \(\chi_{5376}(1331,\cdot)\) \(\chi_{5376}(1499,\cdot)\) \(\chi_{5376}(1667,\cdot)\) \(\chi_{5376}(1835,\cdot)\) \(\chi_{5376}(2003,\cdot)\) \(\chi_{5376}(2171,\cdot)\) \(\chi_{5376}(2339,\cdot)\) \(\chi_{5376}(2507,\cdot)\) \(\chi_{5376}(2675,\cdot)\) \(\chi_{5376}(2843,\cdot)\) \(\chi_{5376}(3011,\cdot)\) \(\chi_{5376}(3179,\cdot)\) \(\chi_{5376}(3347,\cdot)\) \(\chi_{5376}(3515,\cdot)\) \(\chi_{5376}(3683,\cdot)\) \(\chi_{5376}(3851,\cdot)\) \(\chi_{5376}(4019,\cdot)\) \(\chi_{5376}(4187,\cdot)\) \(\chi_{5376}(4355,\cdot)\) \(\chi_{5376}(4523,\cdot)\) \(\chi_{5376}(4691,\cdot)\) \(\chi_{5376}(4859,\cdot)\) \(\chi_{5376}(5027,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((2815,5125,1793,4609)\) → \((-1,e\left(\frac{9}{64}\right),-1,1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5376 }(155, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{33}{64}\right)\) |