Basic properties
Modulus: | \(4029\) | |
Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(312\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1343}(478,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.cx
\(\chi_{4029}(19,\cdot)\) \(\chi_{4029}(25,\cdot)\) \(\chi_{4029}(49,\cdot)\) \(\chi_{4029}(76,\cdot)\) \(\chi_{4029}(121,\cdot)\) \(\chi_{4029}(151,\cdot)\) \(\chi_{4029}(178,\cdot)\) \(\chi_{4029}(202,\cdot)\) \(\chi_{4029}(253,\cdot)\) \(\chi_{4029}(325,\cdot)\) \(\chi_{4029}(400,\cdot)\) \(\chi_{4029}(406,\cdot)\) \(\chi_{4029}(427,\cdot)\) \(\chi_{4029}(478,\cdot)\) \(\chi_{4029}(604,\cdot)\) \(\chi_{4029}(637,\cdot)\) \(\chi_{4029}(682,\cdot)\) \(\chi_{4029}(784,\cdot)\) \(\chi_{4029}(835,\cdot)\) \(\chi_{4029}(841,\cdot)\) \(\chi_{4029}(961,\cdot)\) \(\chi_{4029}(967,\cdot)\) \(\chi_{4029}(988,\cdot)\) \(\chi_{4029}(1063,\cdot)\) \(\chi_{4029}(1069,\cdot)\) \(\chi_{4029}(1198,\cdot)\) \(\chi_{4029}(1216,\cdot)\) \(\chi_{4029}(1273,\cdot)\) \(\chi_{4029}(1300,\cdot)\) \(\chi_{4029}(1345,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{312})$ |
Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{4}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(478, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{229}{312}\right)\) | \(e\left(\frac{19}{312}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{41}{104}\right)\) | \(e\left(\frac{31}{312}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{75}{104}\right)\) | \(e\left(\frac{25}{39}\right)\) |