Basic properties
| Modulus: | \(3380\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3380.cy
\(\chi_{3380}(37,\cdot)\) \(\chi_{3380}(93,\cdot)\) \(\chi_{3380}(137,\cdot)\) \(\chi_{3380}(253,\cdot)\) \(\chi_{3380}(297,\cdot)\) \(\chi_{3380}(353,\cdot)\) \(\chi_{3380}(397,\cdot)\) \(\chi_{3380}(513,\cdot)\) \(\chi_{3380}(557,\cdot)\) \(\chi_{3380}(613,\cdot)\) \(\chi_{3380}(773,\cdot)\) \(\chi_{3380}(817,\cdot)\) \(\chi_{3380}(873,\cdot)\) \(\chi_{3380}(917,\cdot)\) \(\chi_{3380}(1077,\cdot)\) \(\chi_{3380}(1133,\cdot)\) \(\chi_{3380}(1177,\cdot)\) \(\chi_{3380}(1293,\cdot)\) \(\chi_{3380}(1337,\cdot)\) \(\chi_{3380}(1393,\cdot)\) \(\chi_{3380}(1437,\cdot)\) \(\chi_{3380}(1553,\cdot)\) \(\chi_{3380}(1597,\cdot)\) \(\chi_{3380}(1653,\cdot)\) \(\chi_{3380}(1697,\cdot)\) \(\chi_{3380}(1813,\cdot)\) \(\chi_{3380}(1857,\cdot)\) \(\chi_{3380}(1913,\cdot)\) \(\chi_{3380}(1957,\cdot)\) \(\chi_{3380}(2073,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1691,677,1861)\) → \((1,i,e\left(\frac{151}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3380 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{17}{78}\right)\) |