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.bv
\(\chi_{1441}(105,\cdot)\) \(\chi_{1441}(117,\cdot)\) \(\chi_{1441}(151,\cdot)\) \(\chi_{1441}(167,\cdot)\) \(\chi_{1441}(205,\cdot)\) \(\chi_{1441}(233,\cdot)\) \(\chi_{1441}(239,\cdot)\) \(\chi_{1441}(283,\cdot)\) \(\chi_{1441}(310,\cdot)\) \(\chi_{1441}(398,\cdot)\) \(\chi_{1441}(402,\cdot)\) \(\chi_{1441}(420,\cdot)\) \(\chi_{1441}(426,\cdot)\) \(\chi_{1441}(431,\cdot)\) \(\chi_{1441}(437,\cdot)\) \(\chi_{1441}(468,\cdot)\) \(\chi_{1441}(502,\cdot)\) \(\chi_{1441}(567,\cdot)\) \(\chi_{1441}(579,\cdot)\) \(\chi_{1441}(589,\cdot)\) \(\chi_{1441}(601,\cdot)\) \(\chi_{1441}(618,\cdot)\) \(\chi_{1441}(645,\cdot)\) \(\chi_{1441}(662,\cdot)\) \(\chi_{1441}(668,\cdot)\) \(\chi_{1441}(778,\cdot)\) \(\chi_{1441}(798,\cdot)\) \(\chi_{1441}(820,\cdot)\) \(\chi_{1441}(821,\cdot)\) \(\chi_{1441}(827,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{54}{65}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1441 }(1031, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{111}{130}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{31}{65}\right)\) |