Basic properties
Modulus: | \(1183\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | 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 1183.bi
\(\chi_{1183}(16,\cdot)\) \(\chi_{1183}(74,\cdot)\) \(\chi_{1183}(107,\cdot)\) \(\chi_{1183}(165,\cdot)\) \(\chi_{1183}(198,\cdot)\) \(\chi_{1183}(256,\cdot)\) \(\chi_{1183}(289,\cdot)\) \(\chi_{1183}(347,\cdot)\) \(\chi_{1183}(380,\cdot)\) \(\chi_{1183}(438,\cdot)\) \(\chi_{1183}(471,\cdot)\) \(\chi_{1183}(562,\cdot)\) \(\chi_{1183}(620,\cdot)\) \(\chi_{1183}(711,\cdot)\) \(\chi_{1183}(744,\cdot)\) \(\chi_{1183}(802,\cdot)\) \(\chi_{1183}(835,\cdot)\) \(\chi_{1183}(893,\cdot)\) \(\chi_{1183}(926,\cdot)\) \(\chi_{1183}(984,\cdot)\) \(\chi_{1183}(1017,\cdot)\) \(\chi_{1183}(1075,\cdot)\) \(\chi_{1183}(1108,\cdot)\) \(\chi_{1183}(1166,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.2 |
Values on generators
\((339,1016)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{22}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(835, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) |