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.cd
\(\chi_{5780}(47,\cdot)\) \(\chi_{5780}(123,\cdot)\) \(\chi_{5780}(387,\cdot)\) \(\chi_{5780}(463,\cdot)\) \(\chi_{5780}(727,\cdot)\) \(\chi_{5780}(803,\cdot)\) \(\chi_{5780}(1067,\cdot)\) \(\chi_{5780}(1143,\cdot)\) \(\chi_{5780}(1747,\cdot)\) \(\chi_{5780}(1823,\cdot)\) \(\chi_{5780}(2087,\cdot)\) \(\chi_{5780}(2163,\cdot)\) \(\chi_{5780}(2427,\cdot)\) \(\chi_{5780}(2503,\cdot)\) \(\chi_{5780}(2767,\cdot)\) \(\chi_{5780}(2843,\cdot)\) \(\chi_{5780}(3107,\cdot)\) \(\chi_{5780}(3183,\cdot)\) \(\chi_{5780}(3447,\cdot)\) \(\chi_{5780}(3523,\cdot)\) \(\chi_{5780}(3787,\cdot)\) \(\chi_{5780}(3863,\cdot)\) \(\chi_{5780}(4127,\cdot)\) \(\chi_{5780}(4203,\cdot)\) \(\chi_{5780}(4467,\cdot)\) \(\chi_{5780}(4543,\cdot)\) \(\chi_{5780}(4807,\cdot)\) \(\chi_{5780}(4883,\cdot)\) \(\chi_{5780}(5147,\cdot)\) \(\chi_{5780}(5223,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((2891,1157,581)\) → \((-1,i,e\left(\frac{25}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 5780 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{31}{68}\right)\) |