Basic properties
| Modulus: | \(269\) | |
| Conductor: | \(269\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(67\) | 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.d
\(\chi_{269}(5,\cdot)\) \(\chi_{269}(14,\cdot)\) \(\chi_{269}(16,\cdot)\) \(\chi_{269}(21,\cdot)\) \(\chi_{269}(23,\cdot)\) \(\chi_{269}(24,\cdot)\) \(\chi_{269}(25,\cdot)\) \(\chi_{269}(36,\cdot)\) \(\chi_{269}(37,\cdot)\) \(\chi_{269}(38,\cdot)\) \(\chi_{269}(41,\cdot)\) \(\chi_{269}(44,\cdot)\) \(\chi_{269}(47,\cdot)\) \(\chi_{269}(52,\cdot)\) \(\chi_{269}(53,\cdot)\) \(\chi_{269}(54,\cdot)\) \(\chi_{269}(57,\cdot)\) \(\chi_{269}(58,\cdot)\) \(\chi_{269}(61,\cdot)\) \(\chi_{269}(62,\cdot)\) \(\chi_{269}(66,\cdot)\) \(\chi_{269}(67,\cdot)\) \(\chi_{269}(70,\cdot)\) \(\chi_{269}(78,\cdot)\) \(\chi_{269}(80,\cdot)\) \(\chi_{269}(81,\cdot)\) \(\chi_{269}(87,\cdot)\) \(\chi_{269}(93,\cdot)\) \(\chi_{269}(99,\cdot)\) \(\chi_{269}(105,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{67})$ |
| Fixed field: | Number field defined by a degree 67 polynomial |
Values on generators
\(2\) → \(e\left(\frac{33}{67}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 269 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{67}\right)\) | \(e\left(\frac{46}{67}\right)\) | \(e\left(\frac{66}{67}\right)\) | \(e\left(\frac{30}{67}\right)\) | \(e\left(\frac{12}{67}\right)\) | \(e\left(\frac{24}{67}\right)\) | \(e\left(\frac{32}{67}\right)\) | \(e\left(\frac{25}{67}\right)\) | \(e\left(\frac{63}{67}\right)\) | \(e\left(\frac{19}{67}\right)\) |