Basic properties
| Modulus: | \(181\) | |
| Conductor: | \(181\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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 181.r
\(\chi_{181}(2,\cdot)\) \(\chi_{181}(10,\cdot)\) \(\chi_{181}(18,\cdot)\) \(\chi_{181}(21,\cdot)\) \(\chi_{181}(23,\cdot)\) \(\chi_{181}(24,\cdot)\) \(\chi_{181}(28,\cdot)\) \(\chi_{181}(41,\cdot)\) \(\chi_{181}(47,\cdot)\) \(\chi_{181}(50,\cdot)\) \(\chi_{181}(53,\cdot)\) \(\chi_{181}(54,\cdot)\) \(\chi_{181}(57,\cdot)\) \(\chi_{181}(58,\cdot)\) \(\chi_{181}(63,\cdot)\) \(\chi_{181}(66,\cdot)\) \(\chi_{181}(69,\cdot)\) \(\chi_{181}(76,\cdot)\) \(\chi_{181}(77,\cdot)\) \(\chi_{181}(78,\cdot)\) \(\chi_{181}(83,\cdot)\) \(\chi_{181}(84,\cdot)\) \(\chi_{181}(85,\cdot)\) \(\chi_{181}(90,\cdot)\) \(\chi_{181}(91,\cdot)\) \(\chi_{181}(96,\cdot)\) \(\chi_{181}(97,\cdot)\) \(\chi_{181}(98,\cdot)\) \(\chi_{181}(103,\cdot)\) \(\chi_{181}(104,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{180}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 181 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{31}{90}\right)\) |