Basic properties
| Modulus: | \(169\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 169.l
\(\chi_{169}(2,\cdot)\) \(\chi_{169}(6,\cdot)\) \(\chi_{169}(7,\cdot)\) \(\chi_{169}(11,\cdot)\) \(\chi_{169}(15,\cdot)\) \(\chi_{169}(20,\cdot)\) \(\chi_{169}(24,\cdot)\) \(\chi_{169}(28,\cdot)\) \(\chi_{169}(32,\cdot)\) \(\chi_{169}(33,\cdot)\) \(\chi_{169}(37,\cdot)\) \(\chi_{169}(41,\cdot)\) \(\chi_{169}(45,\cdot)\) \(\chi_{169}(46,\cdot)\) \(\chi_{169}(50,\cdot)\) \(\chi_{169}(54,\cdot)\) \(\chi_{169}(58,\cdot)\) \(\chi_{169}(59,\cdot)\) \(\chi_{169}(63,\cdot)\) \(\chi_{169}(67,\cdot)\) \(\chi_{169}(71,\cdot)\) \(\chi_{169}(72,\cdot)\) \(\chi_{169}(76,\cdot)\) \(\chi_{169}(84,\cdot)\) \(\chi_{169}(85,\cdot)\) \(\chi_{169}(93,\cdot)\) \(\chi_{169}(97,\cdot)\) \(\chi_{169}(98,\cdot)\) \(\chi_{169}(102,\cdot)\) \(\chi_{169}(106,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{79}{156}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 169 }(167, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{25}{156}\right)\) |