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.cs
\(\chi_{3380}(7,\cdot)\) \(\chi_{3380}(123,\cdot)\) \(\chi_{3380}(167,\cdot)\) \(\chi_{3380}(223,\cdot)\) \(\chi_{3380}(267,\cdot)\) \(\chi_{3380}(383,\cdot)\) \(\chi_{3380}(483,\cdot)\) \(\chi_{3380}(527,\cdot)\) \(\chi_{3380}(643,\cdot)\) \(\chi_{3380}(687,\cdot)\) \(\chi_{3380}(743,\cdot)\) \(\chi_{3380}(787,\cdot)\) \(\chi_{3380}(903,\cdot)\) \(\chi_{3380}(947,\cdot)\) \(\chi_{3380}(1003,\cdot)\) \(\chi_{3380}(1047,\cdot)\) \(\chi_{3380}(1163,\cdot)\) \(\chi_{3380}(1207,\cdot)\) \(\chi_{3380}(1307,\cdot)\) \(\chi_{3380}(1423,\cdot)\) \(\chi_{3380}(1467,\cdot)\) \(\chi_{3380}(1523,\cdot)\) \(\chi_{3380}(1567,\cdot)\) \(\chi_{3380}(1683,\cdot)\) \(\chi_{3380}(1727,\cdot)\) \(\chi_{3380}(1783,\cdot)\) \(\chi_{3380}(1827,\cdot)\) \(\chi_{3380}(1943,\cdot)\) \(\chi_{3380}(1987,\cdot)\) \(\chi_{3380}(2043,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1691,677,1861)\) → \((-1,i,e\left(\frac{55}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(3027, a) \) | \(-1\) | \(1\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{47}{78}\right)\) |