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.gh
\(\chi_{7605}(92,\cdot)\) \(\chi_{7605}(248,\cdot)\) \(\chi_{7605}(443,\cdot)\) \(\chi_{7605}(482,\cdot)\) \(\chi_{7605}(833,\cdot)\) \(\chi_{7605}(1028,\cdot)\) \(\chi_{7605}(1067,\cdot)\) \(\chi_{7605}(1262,\cdot)\) \(\chi_{7605}(1418,\cdot)\) \(\chi_{7605}(1613,\cdot)\) \(\chi_{7605}(1652,\cdot)\) \(\chi_{7605}(1847,\cdot)\) \(\chi_{7605}(2003,\cdot)\) \(\chi_{7605}(2237,\cdot)\) \(\chi_{7605}(2432,\cdot)\) \(\chi_{7605}(2588,\cdot)\) \(\chi_{7605}(2783,\cdot)\) \(\chi_{7605}(2822,\cdot)\) \(\chi_{7605}(3017,\cdot)\) \(\chi_{7605}(3173,\cdot)\) \(\chi_{7605}(3368,\cdot)\) \(\chi_{7605}(3407,\cdot)\) \(\chi_{7605}(3602,\cdot)\) \(\chi_{7605}(3758,\cdot)\) \(\chi_{7605}(3953,\cdot)\) \(\chi_{7605}(3992,\cdot)\) \(\chi_{7605}(4187,\cdot)\) \(\chi_{7605}(4343,\cdot)\) \(\chi_{7605}(4538,\cdot)\) \(\chi_{7605}(4577,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{11}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(92, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(-1\) | \(e\left(\frac{7}{12}\right)\) |