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.fi
\(\chi_{7605}(94,\cdot)\) \(\chi_{7605}(679,\cdot)\) \(\chi_{7605}(1114,\cdot)\) \(\chi_{7605}(1264,\cdot)\) \(\chi_{7605}(1699,\cdot)\) \(\chi_{7605}(1849,\cdot)\) \(\chi_{7605}(2284,\cdot)\) \(\chi_{7605}(2434,\cdot)\) \(\chi_{7605}(2869,\cdot)\) \(\chi_{7605}(3454,\cdot)\) \(\chi_{7605}(3604,\cdot)\) \(\chi_{7605}(4039,\cdot)\) \(\chi_{7605}(4189,\cdot)\) \(\chi_{7605}(4624,\cdot)\) \(\chi_{7605}(4774,\cdot)\) \(\chi_{7605}(5209,\cdot)\) \(\chi_{7605}(5359,\cdot)\) \(\chi_{7605}(5794,\cdot)\) \(\chi_{7605}(5944,\cdot)\) \(\chi_{7605}(6379,\cdot)\) \(\chi_{7605}(6529,\cdot)\) \(\chi_{7605}(6964,\cdot)\) \(\chi_{7605}(7114,\cdot)\) \(\chi_{7605}(7549,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{16}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(94, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |