Basic properties
Modulus: | \(7605\) | |
Conductor: | \(7605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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 7605.fc
\(\chi_{7605}(79,\cdot)\) \(\chi_{7605}(274,\cdot)\) \(\chi_{7605}(664,\cdot)\) \(\chi_{7605}(859,\cdot)\) \(\chi_{7605}(1249,\cdot)\) \(\chi_{7605}(1444,\cdot)\) \(\chi_{7605}(1834,\cdot)\) \(\chi_{7605}(2419,\cdot)\) \(\chi_{7605}(2614,\cdot)\) \(\chi_{7605}(3004,\cdot)\) \(\chi_{7605}(3199,\cdot)\) \(\chi_{7605}(3589,\cdot)\) \(\chi_{7605}(3784,\cdot)\) \(\chi_{7605}(4174,\cdot)\) \(\chi_{7605}(4369,\cdot)\) \(\chi_{7605}(4759,\cdot)\) \(\chi_{7605}(4954,\cdot)\) \(\chi_{7605}(5344,\cdot)\) \(\chi_{7605}(5539,\cdot)\) \(\chi_{7605}(5929,\cdot)\) \(\chi_{7605}(6124,\cdot)\) \(\chi_{7605}(6514,\cdot)\) \(\chi_{7605}(6709,\cdot)\) \(\chi_{7605}(7294,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{2}{3}\right),-1,e\left(\frac{2}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 7605 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |