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.hd
\(\chi_{7605}(212,\cdot)\) \(\chi_{7605}(218,\cdot)\) \(\chi_{7605}(452,\cdot)\) \(\chi_{7605}(563,\cdot)\) \(\chi_{7605}(797,\cdot)\) \(\chi_{7605}(803,\cdot)\) \(\chi_{7605}(1148,\cdot)\) \(\chi_{7605}(1382,\cdot)\) \(\chi_{7605}(1388,\cdot)\) \(\chi_{7605}(1622,\cdot)\) \(\chi_{7605}(1733,\cdot)\) \(\chi_{7605}(1967,\cdot)\) \(\chi_{7605}(1973,\cdot)\) \(\chi_{7605}(2207,\cdot)\) \(\chi_{7605}(2318,\cdot)\) \(\chi_{7605}(2552,\cdot)\) \(\chi_{7605}(2792,\cdot)\) \(\chi_{7605}(2903,\cdot)\) \(\chi_{7605}(3137,\cdot)\) \(\chi_{7605}(3143,\cdot)\) \(\chi_{7605}(3377,\cdot)\) \(\chi_{7605}(3488,\cdot)\) \(\chi_{7605}(3722,\cdot)\) \(\chi_{7605}(3728,\cdot)\) \(\chi_{7605}(3962,\cdot)\) \(\chi_{7605}(4073,\cdot)\) \(\chi_{7605}(4307,\cdot)\) \(\chi_{7605}(4313,\cdot)\) \(\chi_{7605}(4547,\cdot)\) \(\chi_{7605}(4658,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{35}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 7605 }(1622, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(i\) |