Basic properties
| Modulus: | \(1223\) | |
| Conductor: | \(1223\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1222\) | 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 1223.h
\(\chi_{1223}(5,\cdot)\) \(\chi_{1223}(10,\cdot)\) \(\chi_{1223}(15,\cdot)\) \(\chi_{1223}(19,\cdot)\) \(\chi_{1223}(20,\cdot)\) \(\chi_{1223}(23,\cdot)\) \(\chi_{1223}(30,\cdot)\) \(\chi_{1223}(31,\cdot)\) \(\chi_{1223}(35,\cdot)\) \(\chi_{1223}(37,\cdot)\) \(\chi_{1223}(38,\cdot)\) \(\chi_{1223}(40,\cdot)\) \(\chi_{1223}(45,\cdot)\) \(\chi_{1223}(46,\cdot)\) \(\chi_{1223}(47,\cdot)\) \(\chi_{1223}(55,\cdot)\) \(\chi_{1223}(60,\cdot)\) \(\chi_{1223}(62,\cdot)\) \(\chi_{1223}(65,\cdot)\) \(\chi_{1223}(67,\cdot)\) \(\chi_{1223}(69,\cdot)\) \(\chi_{1223}(70,\cdot)\) \(\chi_{1223}(71,\cdot)\) \(\chi_{1223}(74,\cdot)\) \(\chi_{1223}(79,\cdot)\) \(\chi_{1223}(80,\cdot)\) \(\chi_{1223}(82,\cdot)\) \(\chi_{1223}(83,\cdot)\) \(\chi_{1223}(89,\cdot)\) \(\chi_{1223}(90,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{611})$ |
| Fixed field: | Number field defined by a degree 1222 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1}{1222}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1223 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{232}{611}\right)\) | \(e\left(\frac{6}{47}\right)\) | \(e\left(\frac{464}{611}\right)\) | \(e\left(\frac{1}{1222}\right)\) | \(e\left(\frac{310}{611}\right)\) | \(e\left(\frac{421}{611}\right)\) | \(e\left(\frac{85}{611}\right)\) | \(e\left(\frac{12}{47}\right)\) | \(e\left(\frac{465}{1222}\right)\) | \(e\left(\frac{29}{611}\right)\) |