Basic properties
| Modulus: | \(2563\) | |
| Conductor: | \(2563\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1160\) | 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 2563.be
\(\chi_{2563}(6,\cdot)\) \(\chi_{2563}(17,\cdot)\) \(\chi_{2563}(24,\cdot)\) \(\chi_{2563}(35,\cdot)\) \(\chi_{2563}(39,\cdot)\) \(\chi_{2563}(40,\cdot)\) \(\chi_{2563}(41,\cdot)\) \(\chi_{2563}(57,\cdot)\) \(\chi_{2563}(61,\cdot)\) \(\chi_{2563}(68,\cdot)\) \(\chi_{2563}(73,\cdot)\) \(\chi_{2563}(79,\cdot)\) \(\chi_{2563}(83,\cdot)\) \(\chi_{2563}(84,\cdot)\) \(\chi_{2563}(90,\cdot)\) \(\chi_{2563}(94,\cdot)\) \(\chi_{2563}(95,\cdot)\) \(\chi_{2563}(96,\cdot)\) \(\chi_{2563}(106,\cdot)\) \(\chi_{2563}(118,\cdot)\) \(\chi_{2563}(127,\cdot)\) \(\chi_{2563}(134,\cdot)\) \(\chi_{2563}(138,\cdot)\) \(\chi_{2563}(139,\cdot)\) \(\chi_{2563}(140,\cdot)\) \(\chi_{2563}(145,\cdot)\) \(\chi_{2563}(149,\cdot)\) \(\chi_{2563}(150,\cdot)\) \(\chi_{2563}(151,\cdot)\) \(\chi_{2563}(156,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1160})$ |
| Fixed field: | Number field defined by a degree 1160 polynomial (not computed) |
Values on generators
\((1399,2333)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{73}{232}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2563 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{161}{290}\right)\) | \(e\left(\frac{597}{1160}\right)\) | \(e\left(\frac{16}{145}\right)\) | \(e\left(\frac{601}{1160}\right)\) | \(e\left(\frac{81}{1160}\right)\) | \(e\left(\frac{89}{580}\right)\) | \(e\left(\frac{193}{290}\right)\) | \(e\left(\frac{17}{580}\right)\) | \(e\left(\frac{17}{232}\right)\) | \(e\left(\frac{5}{8}\right)\) |