Basic properties
| Modulus: | \(2527\) | |
| Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(171\) | 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 2527.cc
\(\chi_{2527}(9,\cdot)\) \(\chi_{2527}(23,\cdot)\) \(\chi_{2527}(44,\cdot)\) \(\chi_{2527}(74,\cdot)\) \(\chi_{2527}(81,\cdot)\) \(\chi_{2527}(130,\cdot)\) \(\chi_{2527}(142,\cdot)\) \(\chi_{2527}(156,\cdot)\) \(\chi_{2527}(177,\cdot)\) \(\chi_{2527}(207,\cdot)\) \(\chi_{2527}(214,\cdot)\) \(\chi_{2527}(263,\cdot)\) \(\chi_{2527}(275,\cdot)\) \(\chi_{2527}(289,\cdot)\) \(\chi_{2527}(310,\cdot)\) \(\chi_{2527}(340,\cdot)\) \(\chi_{2527}(347,\cdot)\) \(\chi_{2527}(396,\cdot)\) \(\chi_{2527}(408,\cdot)\) \(\chi_{2527}(422,\cdot)\) \(\chi_{2527}(443,\cdot)\) \(\chi_{2527}(473,\cdot)\) \(\chi_{2527}(480,\cdot)\) \(\chi_{2527}(529,\cdot)\) \(\chi_{2527}(541,\cdot)\) \(\chi_{2527}(555,\cdot)\) \(\chi_{2527}(576,\cdot)\) \(\chi_{2527}(613,\cdot)\) \(\chi_{2527}(662,\cdot)\) \(\chi_{2527}(674,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{65}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2527 }(263, a) \) | \(1\) | \(1\) | \(e\left(\frac{122}{171}\right)\) | \(e\left(\frac{86}{171}\right)\) | \(e\left(\frac{73}{171}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{37}{171}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{1}{171}\right)\) | \(e\left(\frac{40}{171}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) |