Basic properties
| Modulus: | \(2008\) | |
| Conductor: | \(1004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1004}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2008.bb
\(\chi_{2008}(7,\cdot)\) \(\chi_{2008}(15,\cdot)\) \(\chi_{2008}(23,\cdot)\) \(\chi_{2008}(31,\cdot)\) \(\chi_{2008}(39,\cdot)\) \(\chi_{2008}(79,\cdot)\) \(\chi_{2008}(103,\cdot)\) \(\chi_{2008}(119,\cdot)\) \(\chi_{2008}(135,\cdot)\) \(\chi_{2008}(175,\cdot)\) \(\chi_{2008}(207,\cdot)\) \(\chi_{2008}(263,\cdot)\) \(\chi_{2008}(279,\cdot)\) \(\chi_{2008}(287,\cdot)\) \(\chi_{2008}(303,\cdot)\) \(\chi_{2008}(311,\cdot)\) \(\chi_{2008}(319,\cdot)\) \(\chi_{2008}(335,\cdot)\) \(\chi_{2008}(343,\cdot)\) \(\chi_{2008}(359,\cdot)\) \(\chi_{2008}(375,\cdot)\) \(\chi_{2008}(391,\cdot)\) \(\chi_{2008}(407,\cdot)\) \(\chi_{2008}(415,\cdot)\) \(\chi_{2008}(431,\cdot)\) \(\chi_{2008}(447,\cdot)\) \(\chi_{2008}(511,\cdot)\) \(\chi_{2008}(519,\cdot)\) \(\chi_{2008}(543,\cdot)\) \(\chi_{2008}(551,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((503,1005,257)\) → \((-1,1,e\left(\frac{124}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2008 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{93}{250}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{129}{250}\right)\) | \(e\left(\frac{93}{125}\right)\) | \(e\left(\frac{203}{250}\right)\) | \(e\left(\frac{68}{125}\right)\) | \(e\left(\frac{83}{250}\right)\) | \(e\left(\frac{51}{125}\right)\) | \(e\left(\frac{49}{250}\right)\) | \(e\left(\frac{111}{125}\right)\) |