Basic properties
Modulus: | \(1441\) | |
Conductor: | \(1441\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | 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 1441.cc
\(\chi_{1441}(28,\cdot)\) \(\chi_{1441}(35,\cdot)\) \(\chi_{1441}(41,\cdot)\) \(\chi_{1441}(129,\cdot)\) \(\chi_{1441}(134,\cdot)\) \(\chi_{1441}(156,\cdot)\) \(\chi_{1441}(195,\cdot)\) \(\chi_{1441}(266,\cdot)\) \(\chi_{1441}(271,\cdot)\) \(\chi_{1441}(321,\cdot)\) \(\chi_{1441}(337,\cdot)\) \(\chi_{1441}(404,\cdot)\) \(\chi_{1441}(413,\cdot)\) \(\chi_{1441}(436,\cdot)\) \(\chi_{1441}(442,\cdot)\) \(\chi_{1441}(458,\cdot)\) \(\chi_{1441}(501,\cdot)\) \(\chi_{1441}(545,\cdot)\) \(\chi_{1441}(667,\cdot)\) \(\chi_{1441}(688,\cdot)\) \(\chi_{1441}(689,\cdot)\) \(\chi_{1441}(699,\cdot)\) \(\chi_{1441}(755,\cdot)\) \(\chi_{1441}(772,\cdot)\) \(\chi_{1441}(822,\cdot)\) \(\chi_{1441}(832,\cdot)\) \(\chi_{1441}(860,\cdot)\) \(\chi_{1441}(887,\cdot)\) \(\chi_{1441}(888,\cdot)\) \(\chi_{1441}(930,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{33}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(129, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{109}{130}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{37}{65}\right)\) |