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.db
\(\chi_{3380}(59,\cdot)\) \(\chi_{3380}(119,\cdot)\) \(\chi_{3380}(219,\cdot)\) \(\chi_{3380}(279,\cdot)\) \(\chi_{3380}(379,\cdot)\) \(\chi_{3380}(479,\cdot)\) \(\chi_{3380}(539,\cdot)\) \(\chi_{3380}(579,\cdot)\) \(\chi_{3380}(639,\cdot)\) \(\chi_{3380}(739,\cdot)\) \(\chi_{3380}(799,\cdot)\) \(\chi_{3380}(839,\cdot)\) \(\chi_{3380}(899,\cdot)\) \(\chi_{3380}(999,\cdot)\) \(\chi_{3380}(1059,\cdot)\) \(\chi_{3380}(1099,\cdot)\) \(\chi_{3380}(1159,\cdot)\) \(\chi_{3380}(1259,\cdot)\) \(\chi_{3380}(1319,\cdot)\) \(\chi_{3380}(1359,\cdot)\) \(\chi_{3380}(1419,\cdot)\) \(\chi_{3380}(1519,\cdot)\) \(\chi_{3380}(1579,\cdot)\) \(\chi_{3380}(1619,\cdot)\) \(\chi_{3380}(1679,\cdot)\) \(\chi_{3380}(1839,\cdot)\) \(\chi_{3380}(1879,\cdot)\) \(\chi_{3380}(2039,\cdot)\) \(\chi_{3380}(2099,\cdot)\) \(\chi_{3380}(2139,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1691,677,1861)\) → \((-1,-1,e\left(\frac{35}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) |