Basic properties
| Modulus: | \(2535\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(121,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2535.cj
\(\chi_{2535}(121,\cdot)\) \(\chi_{2535}(166,\cdot)\) \(\chi_{2535}(511,\cdot)\) \(\chi_{2535}(556,\cdot)\) \(\chi_{2535}(706,\cdot)\) \(\chi_{2535}(751,\cdot)\) \(\chi_{2535}(901,\cdot)\) \(\chi_{2535}(946,\cdot)\) \(\chi_{2535}(1096,\cdot)\) \(\chi_{2535}(1141,\cdot)\) \(\chi_{2535}(1291,\cdot)\) \(\chi_{2535}(1336,\cdot)\) \(\chi_{2535}(1486,\cdot)\) \(\chi_{2535}(1531,\cdot)\) \(\chi_{2535}(1681,\cdot)\) \(\chi_{2535}(1726,\cdot)\) \(\chi_{2535}(1876,\cdot)\) \(\chi_{2535}(1921,\cdot)\) \(\chi_{2535}(2071,\cdot)\) \(\chi_{2535}(2116,\cdot)\) \(\chi_{2535}(2266,\cdot)\) \(\chi_{2535}(2311,\cdot)\) \(\chi_{2535}(2461,\cdot)\) \(\chi_{2535}(2506,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1691,1522,1861)\) → \((1,1,e\left(\frac{25}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 2535 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |