Basic properties
| Modulus: | \(7605\) | |
| Conductor: | \(7605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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.fy
\(\chi_{7605}(7,\cdot)\) \(\chi_{7605}(448,\cdot)\) \(\chi_{7605}(592,\cdot)\) \(\chi_{7605}(1003,\cdot)\) \(\chi_{7605}(1012,\cdot)\) \(\chi_{7605}(1177,\cdot)\) \(\chi_{7605}(1588,\cdot)\) \(\chi_{7605}(1597,\cdot)\) \(\chi_{7605}(1618,\cdot)\) \(\chi_{7605}(1762,\cdot)\) \(\chi_{7605}(2173,\cdot)\) \(\chi_{7605}(2182,\cdot)\) \(\chi_{7605}(2203,\cdot)\) \(\chi_{7605}(2758,\cdot)\) \(\chi_{7605}(2767,\cdot)\) \(\chi_{7605}(2788,\cdot)\) \(\chi_{7605}(2932,\cdot)\) \(\chi_{7605}(3343,\cdot)\) \(\chi_{7605}(3352,\cdot)\) \(\chi_{7605}(3373,\cdot)\) \(\chi_{7605}(3517,\cdot)\) \(\chi_{7605}(3928,\cdot)\) \(\chi_{7605}(3937,\cdot)\) \(\chi_{7605}(3958,\cdot)\) \(\chi_{7605}(4102,\cdot)\) \(\chi_{7605}(4513,\cdot)\) \(\chi_{7605}(4522,\cdot)\) \(\chi_{7605}(4543,\cdot)\) \(\chi_{7605}(4687,\cdot)\) \(\chi_{7605}(5098,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{107}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) |