Basic properties
| Modulus: | \(6615\) | |
| Conductor: | \(6615\) | 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 6615.hi
\(\chi_{6615}(52,\cdot)\) \(\chi_{6615}(103,\cdot)\) \(\chi_{6615}(292,\cdot)\) \(\chi_{6615}(367,\cdot)\) \(\chi_{6615}(418,\cdot)\) \(\chi_{6615}(493,\cdot)\) \(\chi_{6615}(682,\cdot)\) \(\chi_{6615}(733,\cdot)\) \(\chi_{6615}(808,\cdot)\) \(\chi_{6615}(922,\cdot)\) \(\chi_{6615}(997,\cdot)\) \(\chi_{6615}(1123,\cdot)\) \(\chi_{6615}(1237,\cdot)\) \(\chi_{6615}(1312,\cdot)\) \(\chi_{6615}(1363,\cdot)\) \(\chi_{6615}(1438,\cdot)\) \(\chi_{6615}(1552,\cdot)\) \(\chi_{6615}(1627,\cdot)\) \(\chi_{6615}(1678,\cdot)\) \(\chi_{6615}(1753,\cdot)\) \(\chi_{6615}(1867,\cdot)\) \(\chi_{6615}(1993,\cdot)\) \(\chi_{6615}(2068,\cdot)\) \(\chi_{6615}(2182,\cdot)\) \(\chi_{6615}(2257,\cdot)\) \(\chi_{6615}(2308,\cdot)\) \(\chi_{6615}(2497,\cdot)\) \(\chi_{6615}(2572,\cdot)\) \(\chi_{6615}(2623,\cdot)\) \(\chi_{6615}(2698,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{252})$ |
| Fixed field: | Number field defined by a degree 252 polynomial (not computed) |
Values on generators
\((3431,2647,1081)\) → \((e\left(\frac{2}{9}\right),-i,e\left(\frac{31}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 6615 }(1123, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{252}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{97}{252}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(1\) | \(e\left(\frac{145}{252}\right)\) | \(e\left(\frac{187}{252}\right)\) |