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.fs
\(\chi_{7605}(139,\cdot)\) \(\chi_{7605}(724,\cdot)\) \(\chi_{7605}(1069,\cdot)\) \(\chi_{7605}(1309,\cdot)\) \(\chi_{7605}(1654,\cdot)\) \(\chi_{7605}(1894,\cdot)\) \(\chi_{7605}(2239,\cdot)\) \(\chi_{7605}(2479,\cdot)\) \(\chi_{7605}(2824,\cdot)\) \(\chi_{7605}(3409,\cdot)\) \(\chi_{7605}(3649,\cdot)\) \(\chi_{7605}(3994,\cdot)\) \(\chi_{7605}(4234,\cdot)\) \(\chi_{7605}(4579,\cdot)\) \(\chi_{7605}(4819,\cdot)\) \(\chi_{7605}(5164,\cdot)\) \(\chi_{7605}(5404,\cdot)\) \(\chi_{7605}(5749,\cdot)\) \(\chi_{7605}(5989,\cdot)\) \(\chi_{7605}(6334,\cdot)\) \(\chi_{7605}(6574,\cdot)\) \(\chi_{7605}(6919,\cdot)\) \(\chi_{7605}(7159,\cdot)\) \(\chi_{7605}(7504,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{5}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(3649, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |