Basic properties
Modulus: | \(269\) | |
Conductor: | \(269\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(134\) | 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 269.e
\(\chi_{269}(4,\cdot)\) \(\chi_{269}(6,\cdot)\) \(\chi_{269}(9,\cdot)\) \(\chi_{269}(11,\cdot)\) \(\chi_{269}(13,\cdot)\) \(\chi_{269}(20,\cdot)\) \(\chi_{269}(30,\cdot)\) \(\chi_{269}(34,\cdot)\) \(\chi_{269}(43,\cdot)\) \(\chi_{269}(45,\cdot)\) \(\chi_{269}(49,\cdot)\) \(\chi_{269}(51,\cdot)\) \(\chi_{269}(55,\cdot)\) \(\chi_{269}(56,\cdot)\) \(\chi_{269}(64,\cdot)\) \(\chi_{269}(65,\cdot)\) \(\chi_{269}(73,\cdot)\) \(\chi_{269}(79,\cdot)\) \(\chi_{269}(84,\cdot)\) \(\chi_{269}(89,\cdot)\) \(\chi_{269}(92,\cdot)\) \(\chi_{269}(96,\cdot)\) \(\chi_{269}(97,\cdot)\) \(\chi_{269}(100,\cdot)\) \(\chi_{269}(103,\cdot)\) \(\chi_{269}(126,\cdot)\) \(\chi_{269}(127,\cdot)\) \(\chi_{269}(133,\cdot)\) \(\chi_{269}(138,\cdot)\) \(\chi_{269}(144,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{67})$ |
Fixed field: | Number field defined by a degree 134 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{3}{134}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 269 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{134}\right)\) | \(e\left(\frac{59}{134}\right)\) | \(e\left(\frac{3}{67}\right)\) | \(e\left(\frac{44}{67}\right)\) | \(e\left(\frac{31}{67}\right)\) | \(e\left(\frac{57}{134}\right)\) | \(e\left(\frac{9}{134}\right)\) | \(e\left(\frac{59}{67}\right)\) | \(e\left(\frac{91}{134}\right)\) | \(e\left(\frac{10}{67}\right)\) |