Basic properties
Modulus: | \(6041\) | |
Conductor: | \(6041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(862\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 6041.k
\(\chi_{6041}(13,\cdot)\) \(\chi_{6041}(20,\cdot)\) \(\chi_{6041}(69,\cdot)\) \(\chi_{6041}(83,\cdot)\) \(\chi_{6041}(90,\cdot)\) \(\chi_{6041}(97,\cdot)\) \(\chi_{6041}(104,\cdot)\) \(\chi_{6041}(125,\cdot)\) \(\chi_{6041}(132,\cdot)\) \(\chi_{6041}(139,\cdot)\) \(\chi_{6041}(146,\cdot)\) \(\chi_{6041}(160,\cdot)\) \(\chi_{6041}(167,\cdot)\) \(\chi_{6041}(188,\cdot)\) \(\chi_{6041}(202,\cdot)\) \(\chi_{6041}(209,\cdot)\) \(\chi_{6041}(237,\cdot)\) \(\chi_{6041}(251,\cdot)\) \(\chi_{6041}(265,\cdot)\) \(\chi_{6041}(314,\cdot)\) \(\chi_{6041}(349,\cdot)\) \(\chi_{6041}(356,\cdot)\) \(\chi_{6041}(370,\cdot)\) \(\chi_{6041}(377,\cdot)\) \(\chi_{6041}(391,\cdot)\) \(\chi_{6041}(405,\cdot)\) \(\chi_{6041}(419,\cdot)\) \(\chi_{6041}(454,\cdot)\) \(\chi_{6041}(468,\cdot)\) \(\chi_{6041}(482,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{431})$ |
Fixed field: | Number field defined by a degree 862 polynomial (not computed) |
Values on generators
\((864,4320)\) → \((-1,e\left(\frac{93}{862}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 6041 }(370, a) \) | \(1\) | \(1\) | \(e\left(\frac{375}{431}\right)\) | \(e\left(\frac{43}{862}\right)\) | \(e\left(\frac{319}{431}\right)\) | \(e\left(\frac{262}{431}\right)\) | \(e\left(\frac{793}{862}\right)\) | \(e\left(\frac{263}{431}\right)\) | \(e\left(\frac{43}{431}\right)\) | \(e\left(\frac{206}{431}\right)\) | \(e\left(\frac{437}{862}\right)\) | \(e\left(\frac{681}{862}\right)\) |