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
\(2\) → \(e\left(\frac{115}{134}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 269 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{115}{134}\right)\) | \(e\left(\frac{73}{134}\right)\) | \(e\left(\frac{48}{67}\right)\) | \(e\left(\frac{34}{67}\right)\) | \(e\left(\frac{27}{67}\right)\) | \(e\left(\frac{41}{134}\right)\) | \(e\left(\frac{77}{134}\right)\) | \(e\left(\frac{6}{67}\right)\) | \(e\left(\frac{49}{134}\right)\) | \(e\left(\frac{26}{67}\right)\) |