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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1441.bz
\(\chi_{1441}(18,\cdot)\) \(\chi_{1441}(19,\cdot)\) \(\chi_{1441}(24,\cdot)\) \(\chi_{1441}(51,\cdot)\) \(\chi_{1441}(68,\cdot)\) \(\chi_{1441}(79,\cdot)\) \(\chi_{1441}(149,\cdot)\) \(\chi_{1441}(150,\cdot)\) \(\chi_{1441}(178,\cdot)\) \(\chi_{1441}(182,\cdot)\) \(\chi_{1441}(200,\cdot)\) \(\chi_{1441}(217,\cdot)\) \(\chi_{1441}(281,\cdot)\) \(\chi_{1441}(294,\cdot)\) \(\chi_{1441}(348,\cdot)\) \(\chi_{1441}(354,\cdot)\) \(\chi_{1441}(425,\cdot)\) \(\chi_{1441}(464,\cdot)\) \(\chi_{1441}(479,\cdot)\) \(\chi_{1441}(556,\cdot)\) \(\chi_{1441}(673,\cdot)\) \(\chi_{1441}(679,\cdot)\) \(\chi_{1441}(706,\cdot)\) \(\chi_{1441}(723,\cdot)\) \(\chi_{1441}(734,\cdot)\) \(\chi_{1441}(805,\cdot)\) \(\chi_{1441}(810,\cdot)\) \(\chi_{1441}(833,\cdot)\) \(\chi_{1441}(854,\cdot)\) \(\chi_{1441}(855,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((1311,133)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1441 }(1080, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) |