Basic properties
| Modulus: | \(7605\) | |
| Conductor: | \(1521\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1521}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.ee
\(\chi_{7605}(16,\cdot)\) \(\chi_{7605}(256,\cdot)\) \(\chi_{7605}(601,\cdot)\) \(\chi_{7605}(841,\cdot)\) \(\chi_{7605}(1186,\cdot)\) \(\chi_{7605}(1426,\cdot)\) \(\chi_{7605}(1771,\cdot)\) \(\chi_{7605}(2011,\cdot)\) \(\chi_{7605}(2356,\cdot)\) \(\chi_{7605}(2596,\cdot)\) \(\chi_{7605}(2941,\cdot)\) \(\chi_{7605}(3181,\cdot)\) \(\chi_{7605}(3766,\cdot)\) \(\chi_{7605}(4111,\cdot)\) \(\chi_{7605}(4351,\cdot)\) \(\chi_{7605}(4696,\cdot)\) \(\chi_{7605}(4936,\cdot)\) \(\chi_{7605}(5281,\cdot)\) \(\chi_{7605}(5521,\cdot)\) \(\chi_{7605}(5866,\cdot)\) \(\chi_{7605}(6451,\cdot)\) \(\chi_{7605}(6691,\cdot)\) \(\chi_{7605}(7036,\cdot)\) \(\chi_{7605}(7276,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{2}{3}\right),1,e\left(\frac{1}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |