Basic properties
Modulus: | \(2527\) | |
Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(342\) | 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 2527.cl
\(\chi_{2527}(17,\cdot)\) \(\chi_{2527}(24,\cdot)\) \(\chi_{2527}(47,\cdot)\) \(\chi_{2527}(61,\cdot)\) \(\chi_{2527}(73,\cdot)\) \(\chi_{2527}(82,\cdot)\) \(\chi_{2527}(150,\cdot)\) \(\chi_{2527}(157,\cdot)\) \(\chi_{2527}(180,\cdot)\) \(\chi_{2527}(194,\cdot)\) \(\chi_{2527}(206,\cdot)\) \(\chi_{2527}(215,\cdot)\) \(\chi_{2527}(283,\cdot)\) \(\chi_{2527}(290,\cdot)\) \(\chi_{2527}(313,\cdot)\) \(\chi_{2527}(327,\cdot)\) \(\chi_{2527}(339,\cdot)\) \(\chi_{2527}(348,\cdot)\) \(\chi_{2527}(416,\cdot)\) \(\chi_{2527}(446,\cdot)\) \(\chi_{2527}(472,\cdot)\) \(\chi_{2527}(481,\cdot)\) \(\chi_{2527}(549,\cdot)\) \(\chi_{2527}(556,\cdot)\) \(\chi_{2527}(579,\cdot)\) \(\chi_{2527}(593,\cdot)\) \(\chi_{2527}(605,\cdot)\) \(\chi_{2527}(614,\cdot)\) \(\chi_{2527}(682,\cdot)\) \(\chi_{2527}(689,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{125}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2527 }(290, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{22}{171}\right)\) | \(e\left(\frac{145}{342}\right)\) | \(e\left(\frac{287}{342}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{94}{171}\right)\) | \(e\left(\frac{167}{342}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{103}{114}\right)\) |