Basic properties
Modulus: | \(6008\) | |
Conductor: | \(751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(375\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{751}(289,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.ce
\(\chi_{6008}(9,\cdot)\) \(\chi_{6008}(25,\cdot)\) \(\chi_{6008}(33,\cdot)\) \(\chi_{6008}(65,\cdot)\) \(\chi_{6008}(81,\cdot)\) \(\chi_{6008}(89,\cdot)\) \(\chi_{6008}(97,\cdot)\) \(\chi_{6008}(105,\cdot)\) \(\chi_{6008}(169,\cdot)\) \(\chi_{6008}(201,\cdot)\) \(\chi_{6008}(217,\cdot)\) \(\chi_{6008}(225,\cdot)\) \(\chi_{6008}(233,\cdot)\) \(\chi_{6008}(265,\cdot)\) \(\chi_{6008}(289,\cdot)\) \(\chi_{6008}(297,\cdot)\) \(\chi_{6008}(361,\cdot)\) \(\chi_{6008}(385,\cdot)\) \(\chi_{6008}(401,\cdot)\) \(\chi_{6008}(441,\cdot)\) \(\chi_{6008}(465,\cdot)\) \(\chi_{6008}(529,\cdot)\) \(\chi_{6008}(553,\cdot)\) \(\chi_{6008}(585,\cdot)\) \(\chi_{6008}(593,\cdot)\) \(\chi_{6008}(601,\cdot)\) \(\chi_{6008}(625,\cdot)\) \(\chi_{6008}(641,\cdot)\) \(\chi_{6008}(689,\cdot)\) \(\chi_{6008}(697,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{375})$ |
Fixed field: | Number field defined by a degree 375 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((1,1,e\left(\frac{329}{375}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6008 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{329}{375}\right)\) | \(e\left(\frac{269}{375}\right)\) | \(e\left(\frac{18}{125}\right)\) | \(e\left(\frac{283}{375}\right)\) | \(e\left(\frac{22}{75}\right)\) | \(e\left(\frac{257}{375}\right)\) | \(e\left(\frac{223}{375}\right)\) | \(e\left(\frac{241}{375}\right)\) | \(e\left(\frac{47}{375}\right)\) | \(e\left(\frac{8}{375}\right)\) |