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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.cw
\(\chi_{4029}(53,\cdot)\) \(\chi_{4029}(59,\cdot)\) \(\chi_{4029}(77,\cdot)\) \(\chi_{4029}(161,\cdot)\) \(\chi_{4029}(206,\cdot)\) \(\chi_{4029}(212,\cdot)\) \(\chi_{4029}(314,\cdot)\) \(\chi_{4029}(359,\cdot)\) \(\chi_{4029}(434,\cdot)\) \(\chi_{4029}(461,\cdot)\) \(\chi_{4029}(542,\cdot)\) \(\chi_{4029}(587,\cdot)\) \(\chi_{4029}(638,\cdot)\) \(\chi_{4029}(671,\cdot)\) \(\chi_{4029}(695,\cdot)\) \(\chi_{4029}(740,\cdot)\) \(\chi_{4029}(746,\cdot)\) \(\chi_{4029}(797,\cdot)\) \(\chi_{4029}(818,\cdot)\) \(\chi_{4029}(824,\cdot)\) \(\chi_{4029}(875,\cdot)\) \(\chi_{4029}(899,\cdot)\) \(\chi_{4029}(944,\cdot)\) \(\chi_{4029}(977,\cdot)\) \(\chi_{4029}(995,\cdot)\) \(\chi_{4029}(1001,\cdot)\) \(\chi_{4029}(1022,\cdot)\) \(\chi_{4029}(1097,\cdot)\) \(\chi_{4029}(1154,\cdot)\) \(\chi_{4029}(1181,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{312})$ |
Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{49}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(359, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{257}{312}\right)\) | \(e\left(\frac{287}{312}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{9}{104}\right)\) | \(e\left(\frac{107}{312}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{19}{104}\right)\) | \(e\left(\frac{2}{39}\right)\) |