Basic properties
Modulus: | \(2873\) | |
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 \(\chi_{169}(69,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2873.bw
\(\chi_{2873}(69,\cdot)\) \(\chi_{2873}(205,\cdot)\) \(\chi_{2873}(290,\cdot)\) \(\chi_{2873}(426,\cdot)\) \(\chi_{2873}(511,\cdot)\) \(\chi_{2873}(647,\cdot)\) \(\chi_{2873}(732,\cdot)\) \(\chi_{2873}(953,\cdot)\) \(\chi_{2873}(1089,\cdot)\) \(\chi_{2873}(1174,\cdot)\) \(\chi_{2873}(1310,\cdot)\) \(\chi_{2873}(1395,\cdot)\) \(\chi_{2873}(1531,\cdot)\) \(\chi_{2873}(1616,\cdot)\) \(\chi_{2873}(1752,\cdot)\) \(\chi_{2873}(1973,\cdot)\) \(\chi_{2873}(2058,\cdot)\) \(\chi_{2873}(2194,\cdot)\) \(\chi_{2873}(2279,\cdot)\) \(\chi_{2873}(2415,\cdot)\) \(\chi_{2873}(2500,\cdot)\) \(\chi_{2873}(2636,\cdot)\) \(\chi_{2873}(2721,\cdot)\) \(\chi_{2873}(2857,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((171,2536)\) → \((e\left(\frac{49}{78}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2873 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) |