Basic properties
Modulus: | \(5780\) | |
Conductor: | \(5780\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(68\) | 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 5780.bt
\(\chi_{5780}(183,\cdot)\) \(\chi_{5780}(523,\cdot)\) \(\chi_{5780}(667,\cdot)\) \(\chi_{5780}(863,\cdot)\) \(\chi_{5780}(1007,\cdot)\) \(\chi_{5780}(1203,\cdot)\) \(\chi_{5780}(1347,\cdot)\) \(\chi_{5780}(1543,\cdot)\) \(\chi_{5780}(1687,\cdot)\) \(\chi_{5780}(1883,\cdot)\) \(\chi_{5780}(2027,\cdot)\) \(\chi_{5780}(2223,\cdot)\) \(\chi_{5780}(2367,\cdot)\) \(\chi_{5780}(2707,\cdot)\) \(\chi_{5780}(2903,\cdot)\) \(\chi_{5780}(3047,\cdot)\) \(\chi_{5780}(3243,\cdot)\) \(\chi_{5780}(3387,\cdot)\) \(\chi_{5780}(3583,\cdot)\) \(\chi_{5780}(3727,\cdot)\) \(\chi_{5780}(3923,\cdot)\) \(\chi_{5780}(4067,\cdot)\) \(\chi_{5780}(4263,\cdot)\) \(\chi_{5780}(4407,\cdot)\) \(\chi_{5780}(4603,\cdot)\) \(\chi_{5780}(4747,\cdot)\) \(\chi_{5780}(4943,\cdot)\) \(\chi_{5780}(5087,\cdot)\) \(\chi_{5780}(5283,\cdot)\) \(\chi_{5780}(5427,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{68})$ |
Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((2891,1157,581)\) → \((-1,-i,e\left(\frac{65}{68}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 5780 }(183, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{33}{68}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{67}{68}\right)\) |