Basic properties
| Modulus: | \(5780\) | |
| Conductor: | \(5780\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | 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.cg
\(\chi_{5780}(43,\cdot)\) \(\chi_{5780}(87,\cdot)\) \(\chi_{5780}(263,\cdot)\) \(\chi_{5780}(287,\cdot)\) \(\chi_{5780}(383,\cdot)\) \(\chi_{5780}(427,\cdot)\) \(\chi_{5780}(603,\cdot)\) \(\chi_{5780}(627,\cdot)\) \(\chi_{5780}(723,\cdot)\) \(\chi_{5780}(767,\cdot)\) \(\chi_{5780}(943,\cdot)\) \(\chi_{5780}(967,\cdot)\) \(\chi_{5780}(1063,\cdot)\) \(\chi_{5780}(1107,\cdot)\) \(\chi_{5780}(1283,\cdot)\) \(\chi_{5780}(1307,\cdot)\) \(\chi_{5780}(1403,\cdot)\) \(\chi_{5780}(1447,\cdot)\) \(\chi_{5780}(1623,\cdot)\) \(\chi_{5780}(1647,\cdot)\) \(\chi_{5780}(1743,\cdot)\) \(\chi_{5780}(1787,\cdot)\) \(\chi_{5780}(1963,\cdot)\) \(\chi_{5780}(1987,\cdot)\) \(\chi_{5780}(2083,\cdot)\) \(\chi_{5780}(2127,\cdot)\) \(\chi_{5780}(2303,\cdot)\) \(\chi_{5780}(2327,\cdot)\) \(\chi_{5780}(2423,\cdot)\) \(\chi_{5780}(2643,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((2891,1157,581)\) → \((-1,-i,e\left(\frac{113}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 5780 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{136}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{83}{136}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{101}{136}\right)\) | \(e\left(\frac{49}{136}\right)\) |