Basic properties
Modulus: | \(6008\) | |
Conductor: | \(6008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.ca
\(\chi_{6008}(27,\cdot)\) \(\chi_{6008}(75,\cdot)\) \(\chi_{6008}(99,\cdot)\) \(\chi_{6008}(155,\cdot)\) \(\chi_{6008}(267,\cdot)\) \(\chi_{6008}(275,\cdot)\) \(\chi_{6008}(315,\cdot)\) \(\chi_{6008}(323,\cdot)\) \(\chi_{6008}(363,\cdot)\) \(\chi_{6008}(371,\cdot)\) \(\chi_{6008}(395,\cdot)\) \(\chi_{6008}(491,\cdot)\) \(\chi_{6008}(507,\cdot)\) \(\chi_{6008}(603,\cdot)\) \(\chi_{6008}(619,\cdot)\) \(\chi_{6008}(651,\cdot)\) \(\chi_{6008}(715,\cdot)\) \(\chi_{6008}(811,\cdot)\) \(\chi_{6008}(819,\cdot)\) \(\chi_{6008}(875,\cdot)\) \(\chi_{6008}(907,\cdot)\) \(\chi_{6008}(971,\cdot)\) \(\chi_{6008}(979,\cdot)\) \(\chi_{6008}(1067,\cdot)\) \(\chi_{6008}(1083,\cdot)\) \(\chi_{6008}(1155,\cdot)\) \(\chi_{6008}(1315,\cdot)\) \(\chi_{6008}(1459,\cdot)\) \(\chi_{6008}(1659,\cdot)\) \(\chi_{6008}(1675,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((-1,-1,e\left(\frac{3}{250}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6008 }(1659, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{250}\right)\) | \(e\left(\frac{83}{250}\right)\) | \(e\left(\frac{39}{125}\right)\) | \(e\left(\frac{3}{125}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{149}{250}\right)\) | \(e\left(\frac{43}{125}\right)\) | \(e\left(\frac{237}{250}\right)\) | \(e\left(\frac{27}{125}\right)\) | \(e\left(\frac{81}{250}\right)\) |