Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(263,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.bt
\(\chi_{8281}(263,\cdot)\) \(\chi_{8281}(373,\cdot)\) \(\chi_{8281}(900,\cdot)\) \(\chi_{8281}(1010,\cdot)\) \(\chi_{8281}(1537,\cdot)\) \(\chi_{8281}(1647,\cdot)\) \(\chi_{8281}(2284,\cdot)\) \(\chi_{8281}(2811,\cdot)\) \(\chi_{8281}(2921,\cdot)\) \(\chi_{8281}(3448,\cdot)\) \(\chi_{8281}(3558,\cdot)\) \(\chi_{8281}(4085,\cdot)\) \(\chi_{8281}(4195,\cdot)\) \(\chi_{8281}(4722,\cdot)\) \(\chi_{8281}(4832,\cdot)\) \(\chi_{8281}(5359,\cdot)\) \(\chi_{8281}(5469,\cdot)\) \(\chi_{8281}(5996,\cdot)\) \(\chi_{8281}(6633,\cdot)\) \(\chi_{8281}(6743,\cdot)\) \(\chi_{8281}(7270,\cdot)\) \(\chi_{8281}(7380,\cdot)\) \(\chi_{8281}(7907,\cdot)\) \(\chi_{8281}(8017,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1 |
Values on generators
\((1522,3382)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{16}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(263, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) |