Basic properties
| Modulus: | \(3380\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3380.cl
\(\chi_{3380}(49,\cdot)\) \(\chi_{3380}(69,\cdot)\) \(\chi_{3380}(309,\cdot)\) \(\chi_{3380}(329,\cdot)\) \(\chi_{3380}(569,\cdot)\) \(\chi_{3380}(589,\cdot)\) \(\chi_{3380}(829,\cdot)\) \(\chi_{3380}(849,\cdot)\) \(\chi_{3380}(1089,\cdot)\) \(\chi_{3380}(1109,\cdot)\) \(\chi_{3380}(1349,\cdot)\) \(\chi_{3380}(1369,\cdot)\) \(\chi_{3380}(1609,\cdot)\) \(\chi_{3380}(1629,\cdot)\) \(\chi_{3380}(1869,\cdot)\) \(\chi_{3380}(1889,\cdot)\) \(\chi_{3380}(2129,\cdot)\) \(\chi_{3380}(2149,\cdot)\) \(\chi_{3380}(2409,\cdot)\) \(\chi_{3380}(2649,\cdot)\) \(\chi_{3380}(2669,\cdot)\) \(\chi_{3380}(2909,\cdot)\) \(\chi_{3380}(2929,\cdot)\) \(\chi_{3380}(3169,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1691,677,1861)\) → \((1,-1,e\left(\frac{29}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{34}{39}\right)\) |