Basic properties
Modulus: | \(1183\) | |
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 \(\chi_{169}(140,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1183.bt
\(\chi_{1183}(36,\cdot)\) \(\chi_{1183}(43,\cdot)\) \(\chi_{1183}(127,\cdot)\) \(\chi_{1183}(134,\cdot)\) \(\chi_{1183}(218,\cdot)\) \(\chi_{1183}(225,\cdot)\) \(\chi_{1183}(309,\cdot)\) \(\chi_{1183}(400,\cdot)\) \(\chi_{1183}(407,\cdot)\) \(\chi_{1183}(491,\cdot)\) \(\chi_{1183}(498,\cdot)\) \(\chi_{1183}(582,\cdot)\) \(\chi_{1183}(589,\cdot)\) \(\chi_{1183}(673,\cdot)\) \(\chi_{1183}(680,\cdot)\) \(\chi_{1183}(764,\cdot)\) \(\chi_{1183}(771,\cdot)\) \(\chi_{1183}(855,\cdot)\) \(\chi_{1183}(862,\cdot)\) \(\chi_{1183}(946,\cdot)\) \(\chi_{1183}(953,\cdot)\) \(\chi_{1183}(1044,\cdot)\) \(\chi_{1183}(1128,\cdot)\) \(\chi_{1183}(1135,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((1,e\left(\frac{59}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(309, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) |