Basic properties
| Modulus: | \(4655\) | |
| Conductor: | \(4655\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(252\) | 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 4655.hb
\(\chi_{4655}(138,\cdot)\) \(\chi_{4655}(187,\cdot)\) \(\chi_{4655}(213,\cdot)\) \(\chi_{4655}(332,\cdot)\) \(\chi_{4655}(367,\cdot)\) \(\chi_{4655}(397,\cdot)\) \(\chi_{4655}(453,\cdot)\) \(\chi_{4655}(537,\cdot)\) \(\chi_{4655}(598,\cdot)\) \(\chi_{4655}(612,\cdot)\) \(\chi_{4655}(633,\cdot)\) \(\chi_{4655}(663,\cdot)\) \(\chi_{4655}(878,\cdot)\) \(\chi_{4655}(997,\cdot)\) \(\chi_{4655}(1032,\cdot)\) \(\chi_{4655}(1062,\cdot)\) \(\chi_{4655}(1118,\cdot)\) \(\chi_{4655}(1202,\cdot)\) \(\chi_{4655}(1263,\cdot)\) \(\chi_{4655}(1277,\cdot)\) \(\chi_{4655}(1298,\cdot)\) \(\chi_{4655}(1328,\cdot)\) \(\chi_{4655}(1468,\cdot)\) \(\chi_{4655}(1517,\cdot)\) \(\chi_{4655}(1543,\cdot)\) \(\chi_{4655}(1662,\cdot)\) \(\chi_{4655}(1727,\cdot)\) \(\chi_{4655}(1867,\cdot)\) \(\chi_{4655}(1928,\cdot)\) \(\chi_{4655}(1963,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{252})$ |
| Fixed field: | Number field defined by a degree 252 polynomial (not computed) |
Values on generators
\((932,3041,2206)\) → \((-i,e\left(\frac{17}{42}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 4655 }(663, a) \) | \(1\) | \(1\) | \(e\left(\frac{209}{252}\right)\) | \(e\left(\frac{221}{252}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{97}{252}\right)\) | \(e\left(\frac{20}{63}\right)\) |