Basic properties
Modulus: | \(4029\) | |
Conductor: | \(4029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(312\) | 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 4029.cu
\(\chi_{4029}(2,\cdot)\) \(\chi_{4029}(26,\cdot)\) \(\chi_{4029}(32,\cdot)\) \(\chi_{4029}(83,\cdot)\) \(\chi_{4029}(104,\cdot)\) \(\chi_{4029}(110,\cdot)\) \(\chi_{4029}(128,\cdot)\) \(\chi_{4029}(155,\cdot)\) \(\chi_{4029}(230,\cdot)\) \(\chi_{4029}(257,\cdot)\) \(\chi_{4029}(263,\cdot)\) \(\chi_{4029}(281,\cdot)\) \(\chi_{4029}(287,\cdot)\) \(\chi_{4029}(332,\cdot)\) \(\chi_{4029}(365,\cdot)\) \(\chi_{4029}(389,\cdot)\) \(\chi_{4029}(440,\cdot)\) \(\chi_{4029}(467,\cdot)\) \(\chi_{4029}(485,\cdot)\) \(\chi_{4029}(518,\cdot)\) \(\chi_{4029}(569,\cdot)\) \(\chi_{4029}(593,\cdot)\) \(\chi_{4029}(716,\cdot)\) \(\chi_{4029}(722,\cdot)\) \(\chi_{4029}(920,\cdot)\) \(\chi_{4029}(950,\cdot)\) \(\chi_{4029}(1046,\cdot)\) \(\chi_{4029}(1052,\cdot)\) \(\chi_{4029}(1103,\cdot)\) \(\chi_{4029}(1148,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{312})$ |
Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{2}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{17}{312}\right)\) | \(e\left(\frac{107}{312}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{1}{104}\right)\) | \(e\left(\frac{35}{312}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{31}{104}\right)\) | \(e\left(\frac{32}{39}\right)\) |