Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(5445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | 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 5445.dq
\(\chi_{5445}(58,\cdot)\) \(\chi_{5445}(97,\cdot)\) \(\chi_{5445}(103,\cdot)\) \(\chi_{5445}(157,\cdot)\) \(\chi_{5445}(223,\cdot)\) \(\chi_{5445}(247,\cdot)\) \(\chi_{5445}(268,\cdot)\) \(\chi_{5445}(313,\cdot)\) \(\chi_{5445}(322,\cdot)\) \(\chi_{5445}(328,\cdot)\) \(\chi_{5445}(367,\cdot)\) \(\chi_{5445}(412,\cdot)\) \(\chi_{5445}(427,\cdot)\) \(\chi_{5445}(553,\cdot)\) \(\chi_{5445}(592,\cdot)\) \(\chi_{5445}(598,\cdot)\) \(\chi_{5445}(643,\cdot)\) \(\chi_{5445}(652,\cdot)\) \(\chi_{5445}(697,\cdot)\) \(\chi_{5445}(718,\cdot)\) \(\chi_{5445}(742,\cdot)\) \(\chi_{5445}(763,\cdot)\) \(\chi_{5445}(808,\cdot)\) \(\chi_{5445}(817,\cdot)\) \(\chi_{5445}(823,\cdot)\) \(\chi_{5445}(862,\cdot)\) \(\chi_{5445}(907,\cdot)\) \(\chi_{5445}(922,\cdot)\) \(\chi_{5445}(988,\cdot)\) \(\chi_{5445}(1048,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{9}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(58, a) \) | \(-1\) | \(1\) | \(e\left(\frac{163}{660}\right)\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{151}{660}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{293}{660}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{49}{132}\right)\) |