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.bo
\(\chi_{1441}(37,\cdot)\) \(\chi_{1441}(82,\cdot)\) \(\chi_{1441}(157,\cdot)\) \(\chi_{1441}(203,\cdot)\) \(\chi_{1441}(218,\cdot)\) \(\chi_{1441}(224,\cdot)\) \(\chi_{1441}(229,\cdot)\) \(\chi_{1441}(235,\cdot)\) \(\chi_{1441}(257,\cdot)\) \(\chi_{1441}(258,\cdot)\) \(\chi_{1441}(345,\cdot)\) \(\chi_{1441}(368,\cdot)\) \(\chi_{1441}(372,\cdot)\) \(\chi_{1441}(377,\cdot)\) \(\chi_{1441}(390,\cdot)\) \(\chi_{1441}(416,\cdot)\) \(\chi_{1441}(422,\cdot)\) \(\chi_{1441}(488,\cdot)\) \(\chi_{1441}(489,\cdot)\) \(\chi_{1441}(504,\cdot)\) \(\chi_{1441}(564,\cdot)\) \(\chi_{1441}(665,\cdot)\) \(\chi_{1441}(685,\cdot)\) \(\chi_{1441}(709,\cdot)\) \(\chi_{1441}(731,\cdot)\) \(\chi_{1441}(740,\cdot)\) \(\chi_{1441}(808,\cdot)\) \(\chi_{1441}(817,\cdot)\) \(\chi_{1441}(883,\cdot)\) \(\chi_{1441}(889,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{7}{130}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(390, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{64}{65}\right)\) |