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.hr
\(\chi_{7605}(58,\cdot)\) \(\chi_{7605}(202,\cdot)\) \(\chi_{7605}(223,\cdot)\) \(\chi_{7605}(232,\cdot)\) \(\chi_{7605}(643,\cdot)\) \(\chi_{7605}(787,\cdot)\) \(\chi_{7605}(808,\cdot)\) \(\chi_{7605}(817,\cdot)\) \(\chi_{7605}(1228,\cdot)\) \(\chi_{7605}(1372,\cdot)\) \(\chi_{7605}(1393,\cdot)\) \(\chi_{7605}(1402,\cdot)\) \(\chi_{7605}(1813,\cdot)\) \(\chi_{7605}(1957,\cdot)\) \(\chi_{7605}(1978,\cdot)\) \(\chi_{7605}(1987,\cdot)\) \(\chi_{7605}(2398,\cdot)\) \(\chi_{7605}(2542,\cdot)\) \(\chi_{7605}(2563,\cdot)\) \(\chi_{7605}(2572,\cdot)\) \(\chi_{7605}(2983,\cdot)\) \(\chi_{7605}(3127,\cdot)\) \(\chi_{7605}(3148,\cdot)\) \(\chi_{7605}(3157,\cdot)\) \(\chi_{7605}(3712,\cdot)\) \(\chi_{7605}(3733,\cdot)\) \(\chi_{7605}(3742,\cdot)\) \(\chi_{7605}(4153,\cdot)\) \(\chi_{7605}(4297,\cdot)\) \(\chi_{7605}(4318,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{61}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(223, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) |