Basic properties
| Modulus: | \(6008\) | |
| Conductor: | \(6008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.cb
\(\chi_{6008}(45,\cdot)\) \(\chi_{6008}(93,\cdot)\) \(\chi_{6008}(125,\cdot)\) \(\chi_{6008}(165,\cdot)\) \(\chi_{6008}(189,\cdot)\) \(\chi_{6008}(237,\cdot)\) \(\chi_{6008}(341,\cdot)\) \(\chi_{6008}(429,\cdot)\) \(\chi_{6008}(445,\cdot)\) \(\chi_{6008}(493,\cdot)\) \(\chi_{6008}(525,\cdot)\) \(\chi_{6008}(605,\cdot)\) \(\chi_{6008}(693,\cdot)\) \(\chi_{6008}(789,\cdot)\) \(\chi_{6008}(797,\cdot)\) \(\chi_{6008}(845,\cdot)\) \(\chi_{6008}(869,\cdot)\) \(\chi_{6008}(997,\cdot)\) \(\chi_{6008}(1005,\cdot)\) \(\chi_{6008}(1013,\cdot)\) \(\chi_{6008}(1085,\cdot)\) \(\chi_{6008}(1157,\cdot)\) \(\chi_{6008}(1181,\cdot)\) \(\chi_{6008}(1261,\cdot)\) \(\chi_{6008}(1365,\cdot)\) \(\chi_{6008}(1573,\cdot)\) \(\chi_{6008}(1653,\cdot)\) \(\chi_{6008}(1693,\cdot)\) \(\chi_{6008}(1709,\cdot)\) \(\chi_{6008}(1773,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((1,-1,e\left(\frac{24}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6008 }(1157, a) \) | \(1\) | \(1\) | \(e\left(\frac{173}{250}\right)\) | \(e\left(\frac{203}{250}\right)\) | \(e\left(\frac{124}{125}\right)\) | \(e\left(\frac{48}{125}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{9}{250}\right)\) | \(e\left(\frac{63}{125}\right)\) | \(e\left(\frac{21}{125}\right)\) | \(e\left(\frac{239}{250}\right)\) | \(e\left(\frac{171}{250}\right)\) |