Basic properties
Modulus: | \(2008\) | |
Conductor: | \(2008\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2008.bf
\(\chi_{2008}(29,\cdot)\) \(\chi_{2008}(37,\cdot)\) \(\chi_{2008}(53,\cdot)\) \(\chi_{2008}(61,\cdot)\) \(\chi_{2008}(77,\cdot)\) \(\chi_{2008}(109,\cdot)\) \(\chi_{2008}(133,\cdot)\) \(\chi_{2008}(141,\cdot)\) \(\chi_{2008}(165,\cdot)\) \(\chi_{2008}(213,\cdot)\) \(\chi_{2008}(229,\cdot)\) \(\chi_{2008}(269,\cdot)\) \(\chi_{2008}(277,\cdot)\) \(\chi_{2008}(285,\cdot)\) \(\chi_{2008}(293,\cdot)\) \(\chi_{2008}(333,\cdot)\) \(\chi_{2008}(341,\cdot)\) \(\chi_{2008}(349,\cdot)\) \(\chi_{2008}(381,\cdot)\) \(\chi_{2008}(397,\cdot)\) \(\chi_{2008}(413,\cdot)\) \(\chi_{2008}(421,\cdot)\) \(\chi_{2008}(429,\cdot)\) \(\chi_{2008}(437,\cdot)\) \(\chi_{2008}(453,\cdot)\) \(\chi_{2008}(461,\cdot)\) \(\chi_{2008}(485,\cdot)\) \(\chi_{2008}(493,\cdot)\) \(\chi_{2008}(557,\cdot)\) \(\chi_{2008}(573,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((503,1005,257)\) → \((1,-1,e\left(\frac{83}{250}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2008 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{203}{250}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{42}{125}\right)\) | \(e\left(\frac{78}{125}\right)\) | \(e\left(\frac{69}{125}\right)\) | \(e\left(\frac{231}{250}\right)\) | \(e\left(\frac{59}{125}\right)\) | \(e\left(\frac{71}{125}\right)\) | \(e\left(\frac{77}{125}\right)\) | \(e\left(\frac{37}{250}\right)\) |