Basic properties
Modulus: | \(6008\) | |
Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(125\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{751}(681,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.bp
\(\chi_{6008}(49,\cdot)\) \(\chi_{6008}(185,\cdot)\) \(\chi_{6008}(249,\cdot)\) \(\chi_{6008}(305,\cdot)\) \(\chi_{6008}(433,\cdot)\) \(\chi_{6008}(457,\cdot)\) \(\chi_{6008}(545,\cdot)\) \(\chi_{6008}(617,\cdot)\) \(\chi_{6008}(681,\cdot)\) \(\chi_{6008}(729,\cdot)\) \(\chi_{6008}(745,\cdot)\) \(\chi_{6008}(761,\cdot)\) \(\chi_{6008}(777,\cdot)\) \(\chi_{6008}(793,\cdot)\) \(\chi_{6008}(905,\cdot)\) \(\chi_{6008}(1145,\cdot)\) \(\chi_{6008}(1241,\cdot)\) \(\chi_{6008}(1281,\cdot)\) \(\chi_{6008}(1329,\cdot)\) \(\chi_{6008}(1345,\cdot)\) \(\chi_{6008}(1545,\cdot)\) \(\chi_{6008}(1689,\cdot)\) \(\chi_{6008}(1849,\cdot)\) \(\chi_{6008}(1921,\cdot)\) \(\chi_{6008}(1937,\cdot)\) \(\chi_{6008}(2025,\cdot)\) \(\chi_{6008}(2033,\cdot)\) \(\chi_{6008}(2097,\cdot)\) \(\chi_{6008}(2129,\cdot)\) \(\chi_{6008}(2185,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((1,1,e\left(\frac{113}{125}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6008 }(681, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{125}\right)\) | \(e\left(\frac{43}{125}\right)\) | \(e\left(\frac{63}{125}\right)\) | \(e\left(\frac{101}{125}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{29}{125}\right)\) | \(e\left(\frac{31}{125}\right)\) | \(e\left(\frac{52}{125}\right)\) | \(e\left(\frac{34}{125}\right)\) | \(e\left(\frac{51}{125}\right)\) |