Basic properties
| Modulus: | \(2008\) | |
| Conductor: | \(251\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{251}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2008.z
\(\chi_{2008}(33,\cdot)\) \(\chi_{2008}(57,\cdot)\) \(\chi_{2008}(97,\cdot)\) \(\chi_{2008}(129,\cdot)\) \(\chi_{2008}(137,\cdot)\) \(\chi_{2008}(145,\cdot)\) \(\chi_{2008}(177,\cdot)\) \(\chi_{2008}(185,\cdot)\) \(\chi_{2008}(193,\cdot)\) \(\chi_{2008}(257,\cdot)\) \(\chi_{2008}(265,\cdot)\) \(\chi_{2008}(281,\cdot)\) \(\chi_{2008}(297,\cdot)\) \(\chi_{2008}(305,\cdot)\) \(\chi_{2008}(313,\cdot)\) \(\chi_{2008}(321,\cdot)\) \(\chi_{2008}(329,\cdot)\) \(\chi_{2008}(385,\cdot)\) \(\chi_{2008}(401,\cdot)\) \(\chi_{2008}(409,\cdot)\) \(\chi_{2008}(417,\cdot)\) \(\chi_{2008}(457,\cdot)\) \(\chi_{2008}(481,\cdot)\) \(\chi_{2008}(489,\cdot)\) \(\chi_{2008}(513,\cdot)\) \(\chi_{2008}(521,\cdot)\) \(\chi_{2008}(545,\cdot)\) \(\chi_{2008}(561,\cdot)\) \(\chi_{2008}(601,\cdot)\) \(\chi_{2008}(609,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((503,1005,257)\) → \((1,1,e\left(\frac{227}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2008 }(33, a) \) | \(-1\) | \(1\) | \(e\left(\frac{66}{125}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{23}{125}\right)\) | \(e\left(\frac{7}{125}\right)\) | \(e\left(\frac{147}{250}\right)\) | \(e\left(\frac{32}{125}\right)\) | \(e\left(\frac{71}{125}\right)\) | \(e\left(\frac{24}{125}\right)\) | \(e\left(\frac{1}{250}\right)\) | \(e\left(\frac{89}{125}\right)\) |