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.br
\(\chi_{1441}(39,\cdot)\) \(\chi_{1441}(52,\cdot)\) \(\chi_{1441}(62,\cdot)\) \(\chi_{1441}(63,\cdot)\) \(\chi_{1441}(84,\cdot)\) \(\chi_{1441}(107,\cdot)\) \(\chi_{1441}(112,\cdot)\) \(\chi_{1441}(183,\cdot)\) \(\chi_{1441}(193,\cdot)\) \(\chi_{1441}(194,\cdot)\) \(\chi_{1441}(211,\cdot)\) \(\chi_{1441}(215,\cdot)\) \(\chi_{1441}(238,\cdot)\) \(\chi_{1441}(244,\cdot)\) \(\chi_{1441}(314,\cdot)\) \(\chi_{1441}(325,\cdot)\) \(\chi_{1441}(369,\cdot)\) \(\chi_{1441}(453,\cdot)\) \(\chi_{1441}(492,\cdot)\) \(\chi_{1441}(563,\cdot)\) \(\chi_{1441}(569,\cdot)\) \(\chi_{1441}(623,\cdot)\) \(\chi_{1441}(700,\cdot)\) \(\chi_{1441}(717,\cdot)\) \(\chi_{1441}(739,\cdot)\) \(\chi_{1441}(754,\cdot)\) \(\chi_{1441}(767,\cdot)\) \(\chi_{1441}(831,\cdot)\) \(\chi_{1441}(838,\cdot)\) \(\chi_{1441}(849,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{8}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1441 }(1030, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) |