Basic properties
| Modulus: | \(1805\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1805.bc
\(\chi_{1805}(6,\cdot)\) \(\chi_{1805}(16,\cdot)\) \(\chi_{1805}(36,\cdot)\) \(\chi_{1805}(61,\cdot)\) \(\chi_{1805}(66,\cdot)\) \(\chi_{1805}(81,\cdot)\) \(\chi_{1805}(101,\cdot)\) \(\chi_{1805}(111,\cdot)\) \(\chi_{1805}(131,\cdot)\) \(\chi_{1805}(156,\cdot)\) \(\chi_{1805}(161,\cdot)\) \(\chi_{1805}(176,\cdot)\) \(\chi_{1805}(196,\cdot)\) \(\chi_{1805}(206,\cdot)\) \(\chi_{1805}(226,\cdot)\) \(\chi_{1805}(251,\cdot)\) \(\chi_{1805}(256,\cdot)\) \(\chi_{1805}(271,\cdot)\) \(\chi_{1805}(291,\cdot)\) \(\chi_{1805}(301,\cdot)\) \(\chi_{1805}(321,\cdot)\) \(\chi_{1805}(346,\cdot)\) \(\chi_{1805}(351,\cdot)\) \(\chi_{1805}(366,\cdot)\) \(\chi_{1805}(386,\cdot)\) \(\chi_{1805}(396,\cdot)\) \(\chi_{1805}(416,\cdot)\) \(\chi_{1805}(441,\cdot)\) \(\chi_{1805}(446,\cdot)\) \(\chi_{1805}(461,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((362,1446)\) → \((1,e\left(\frac{70}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1805 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{70}{171}\right)\) | \(e\left(\frac{154}{171}\right)\) | \(e\left(\frac{140}{171}\right)\) | \(e\left(\frac{53}{171}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{137}{171}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{116}{171}\right)\) |