Basic properties
Modulus: | \(1183\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.bp
\(\chi_{1183}(30,\cdot)\) \(\chi_{1183}(88,\cdot)\) \(\chi_{1183}(121,\cdot)\) \(\chi_{1183}(179,\cdot)\) \(\chi_{1183}(212,\cdot)\) \(\chi_{1183}(270,\cdot)\) \(\chi_{1183}(303,\cdot)\) \(\chi_{1183}(394,\cdot)\) \(\chi_{1183}(452,\cdot)\) \(\chi_{1183}(543,\cdot)\) \(\chi_{1183}(576,\cdot)\) \(\chi_{1183}(634,\cdot)\) \(\chi_{1183}(667,\cdot)\) \(\chi_{1183}(725,\cdot)\) \(\chi_{1183}(758,\cdot)\) \(\chi_{1183}(816,\cdot)\) \(\chi_{1183}(849,\cdot)\) \(\chi_{1183}(907,\cdot)\) \(\chi_{1183}(940,\cdot)\) \(\chi_{1183}(998,\cdot)\) \(\chi_{1183}(1031,\cdot)\) \(\chi_{1183}(1089,\cdot)\) \(\chi_{1183}(1122,\cdot)\) \(\chi_{1183}(1180,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,1016)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{71}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(1089, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{1}{39}\right)\) |