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.fp
\(\chi_{7605}(259,\cdot)\) \(\chi_{7605}(454,\cdot)\) \(\chi_{7605}(1039,\cdot)\) \(\chi_{7605}(1429,\cdot)\) \(\chi_{7605}(1624,\cdot)\) \(\chi_{7605}(2014,\cdot)\) \(\chi_{7605}(2209,\cdot)\) \(\chi_{7605}(2599,\cdot)\) \(\chi_{7605}(2794,\cdot)\) \(\chi_{7605}(3184,\cdot)\) \(\chi_{7605}(3769,\cdot)\) \(\chi_{7605}(3964,\cdot)\) \(\chi_{7605}(4354,\cdot)\) \(\chi_{7605}(4549,\cdot)\) \(\chi_{7605}(4939,\cdot)\) \(\chi_{7605}(5134,\cdot)\) \(\chi_{7605}(5524,\cdot)\) \(\chi_{7605}(5719,\cdot)\) \(\chi_{7605}(6109,\cdot)\) \(\chi_{7605}(6304,\cdot)\) \(\chi_{7605}(6694,\cdot)\) \(\chi_{7605}(6889,\cdot)\) \(\chi_{7605}(7279,\cdot)\) \(\chi_{7605}(7474,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{2}{3}\right),-1,e\left(\frac{9}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(1429, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |