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.ha
\(\chi_{7605}(38,\cdot)\) \(\chi_{7605}(77,\cdot)\) \(\chi_{7605}(272,\cdot)\) \(\chi_{7605}(428,\cdot)\) \(\chi_{7605}(623,\cdot)\) \(\chi_{7605}(662,\cdot)\) \(\chi_{7605}(857,\cdot)\) \(\chi_{7605}(1208,\cdot)\) \(\chi_{7605}(1247,\cdot)\) \(\chi_{7605}(1442,\cdot)\) \(\chi_{7605}(1598,\cdot)\) \(\chi_{7605}(1793,\cdot)\) \(\chi_{7605}(1832,\cdot)\) \(\chi_{7605}(2183,\cdot)\) \(\chi_{7605}(2378,\cdot)\) \(\chi_{7605}(2417,\cdot)\) \(\chi_{7605}(2612,\cdot)\) \(\chi_{7605}(2768,\cdot)\) \(\chi_{7605}(2963,\cdot)\) \(\chi_{7605}(3002,\cdot)\) \(\chi_{7605}(3197,\cdot)\) \(\chi_{7605}(3353,\cdot)\) \(\chi_{7605}(3587,\cdot)\) \(\chi_{7605}(3782,\cdot)\) \(\chi_{7605}(3938,\cdot)\) \(\chi_{7605}(4133,\cdot)\) \(\chi_{7605}(4172,\cdot)\) \(\chi_{7605}(4367,\cdot)\) \(\chi_{7605}(4523,\cdot)\) \(\chi_{7605}(4718,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{11}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(38, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) |