Basic properties
| Modulus: | \(2366\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2366.bx
\(\chi_{2366}(43,\cdot)\) \(\chi_{2366}(127,\cdot)\) \(\chi_{2366}(225,\cdot)\) \(\chi_{2366}(309,\cdot)\) \(\chi_{2366}(407,\cdot)\) \(\chi_{2366}(491,\cdot)\) \(\chi_{2366}(589,\cdot)\) \(\chi_{2366}(673,\cdot)\) \(\chi_{2366}(771,\cdot)\) \(\chi_{2366}(855,\cdot)\) \(\chi_{2366}(953,\cdot)\) \(\chi_{2366}(1135,\cdot)\) \(\chi_{2366}(1219,\cdot)\) \(\chi_{2366}(1317,\cdot)\) \(\chi_{2366}(1401,\cdot)\) \(\chi_{2366}(1583,\cdot)\) \(\chi_{2366}(1681,\cdot)\) \(\chi_{2366}(1765,\cdot)\) \(\chi_{2366}(1863,\cdot)\) \(\chi_{2366}(1947,\cdot)\) \(\chi_{2366}(2045,\cdot)\) \(\chi_{2366}(2129,\cdot)\) \(\chi_{2366}(2227,\cdot)\) \(\chi_{2366}(2311,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,2199)\) → \((1,e\left(\frac{61}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 2366 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) |