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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3380.cz
\(\chi_{3380}(63,\cdot)\) \(\chi_{3380}(67,\cdot)\) \(\chi_{3380}(163,\cdot)\) \(\chi_{3380}(227,\cdot)\) \(\chi_{3380}(323,\cdot)\) \(\chi_{3380}(327,\cdot)\) \(\chi_{3380}(423,\cdot)\) \(\chi_{3380}(487,\cdot)\) \(\chi_{3380}(583,\cdot)\) \(\chi_{3380}(683,\cdot)\) \(\chi_{3380}(747,\cdot)\) \(\chi_{3380}(843,\cdot)\) \(\chi_{3380}(847,\cdot)\) \(\chi_{3380}(943,\cdot)\) \(\chi_{3380}(1007,\cdot)\) \(\chi_{3380}(1107,\cdot)\) \(\chi_{3380}(1203,\cdot)\) \(\chi_{3380}(1267,\cdot)\) \(\chi_{3380}(1363,\cdot)\) \(\chi_{3380}(1367,\cdot)\) \(\chi_{3380}(1463,\cdot)\) \(\chi_{3380}(1527,\cdot)\) \(\chi_{3380}(1623,\cdot)\) \(\chi_{3380}(1627,\cdot)\) \(\chi_{3380}(1723,\cdot)\) \(\chi_{3380}(1787,\cdot)\) \(\chi_{3380}(1883,\cdot)\) \(\chi_{3380}(1887,\cdot)\) \(\chi_{3380}(1983,\cdot)\) \(\chi_{3380}(2143,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1691,677,1861)\) → \((-1,i,e\left(\frac{121}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(1627, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{41}{78}\right)\) |