Basic properties
| Modulus: | \(2366\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2366.bn
\(\chi_{2366}(83,\cdot)\) \(\chi_{2366}(125,\cdot)\) \(\chi_{2366}(265,\cdot)\) \(\chi_{2366}(307,\cdot)\) \(\chi_{2366}(447,\cdot)\) \(\chi_{2366}(489,\cdot)\) \(\chi_{2366}(629,\cdot)\) \(\chi_{2366}(671,\cdot)\) \(\chi_{2366}(811,\cdot)\) \(\chi_{2366}(853,\cdot)\) \(\chi_{2366}(993,\cdot)\) \(\chi_{2366}(1035,\cdot)\) \(\chi_{2366}(1175,\cdot)\) \(\chi_{2366}(1217,\cdot)\) \(\chi_{2366}(1357,\cdot)\) \(\chi_{2366}(1399,\cdot)\) \(\chi_{2366}(1539,\cdot)\) \(\chi_{2366}(1581,\cdot)\) \(\chi_{2366}(1721,\cdot)\) \(\chi_{2366}(1763,\cdot)\) \(\chi_{2366}(1903,\cdot)\) \(\chi_{2366}(1945,\cdot)\) \(\chi_{2366}(2085,\cdot)\) \(\chi_{2366}(2309,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((339,2199)\) → \((-1,e\left(\frac{15}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2366 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{21}{26}\right)\) |