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.gb
\(\chi_{7605}(112,\cdot)\) \(\chi_{7605}(148,\cdot)\) \(\chi_{7605}(502,\cdot)\) \(\chi_{7605}(538,\cdot)\) \(\chi_{7605}(697,\cdot)\) \(\chi_{7605}(733,\cdot)\) \(\chi_{7605}(1087,\cdot)\) \(\chi_{7605}(1123,\cdot)\) \(\chi_{7605}(1318,\cdot)\) \(\chi_{7605}(1672,\cdot)\) \(\chi_{7605}(1708,\cdot)\) \(\chi_{7605}(1867,\cdot)\) \(\chi_{7605}(1903,\cdot)\) \(\chi_{7605}(2257,\cdot)\) \(\chi_{7605}(2293,\cdot)\) \(\chi_{7605}(2452,\cdot)\) \(\chi_{7605}(2488,\cdot)\) \(\chi_{7605}(2842,\cdot)\) \(\chi_{7605}(2878,\cdot)\) \(\chi_{7605}(3037,\cdot)\) \(\chi_{7605}(3073,\cdot)\) \(\chi_{7605}(3427,\cdot)\) \(\chi_{7605}(3463,\cdot)\) \(\chi_{7605}(3622,\cdot)\) \(\chi_{7605}(3658,\cdot)\) \(\chi_{7605}(4012,\cdot)\) \(\chi_{7605}(4048,\cdot)\) \(\chi_{7605}(4207,\cdot)\) \(\chi_{7605}(4243,\cdot)\) \(\chi_{7605}(4597,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{19}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 7605 }(1123, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(i\) | \(e\left(\frac{1}{12}\right)\) |