Basic properties
| Modulus: | \(3380\) | |
| Conductor: | \(3380\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 3380.cu
\(\chi_{3380}(3,\cdot)\) \(\chi_{3380}(87,\cdot)\) \(\chi_{3380}(107,\cdot)\) \(\chi_{3380}(243,\cdot)\) \(\chi_{3380}(263,\cdot)\) \(\chi_{3380}(347,\cdot)\) \(\chi_{3380}(367,\cdot)\) \(\chi_{3380}(503,\cdot)\) \(\chi_{3380}(523,\cdot)\) \(\chi_{3380}(607,\cdot)\) \(\chi_{3380}(627,\cdot)\) \(\chi_{3380}(763,\cdot)\) \(\chi_{3380}(783,\cdot)\) \(\chi_{3380}(887,\cdot)\) \(\chi_{3380}(1023,\cdot)\) \(\chi_{3380}(1043,\cdot)\) \(\chi_{3380}(1127,\cdot)\) \(\chi_{3380}(1147,\cdot)\) \(\chi_{3380}(1283,\cdot)\) \(\chi_{3380}(1303,\cdot)\) \(\chi_{3380}(1387,\cdot)\) \(\chi_{3380}(1407,\cdot)\) \(\chi_{3380}(1563,\cdot)\) \(\chi_{3380}(1647,\cdot)\) \(\chi_{3380}(1803,\cdot)\) \(\chi_{3380}(1823,\cdot)\) \(\chi_{3380}(1907,\cdot)\) \(\chi_{3380}(1927,\cdot)\) \(\chi_{3380}(2063,\cdot)\) \(\chi_{3380}(2083,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1691,677,1861)\) → \((-1,-i,e\left(\frac{31}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{23}{78}\right)\) |