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.gz
\(\chi_{7605}(173,\cdot)\) \(\chi_{7605}(257,\cdot)\) \(\chi_{7605}(407,\cdot)\) \(\chi_{7605}(608,\cdot)\) \(\chi_{7605}(758,\cdot)\) \(\chi_{7605}(842,\cdot)\) \(\chi_{7605}(1193,\cdot)\) \(\chi_{7605}(1343,\cdot)\) \(\chi_{7605}(1427,\cdot)\) \(\chi_{7605}(1577,\cdot)\) \(\chi_{7605}(1778,\cdot)\) \(\chi_{7605}(1928,\cdot)\) \(\chi_{7605}(2012,\cdot)\) \(\chi_{7605}(2162,\cdot)\) \(\chi_{7605}(2363,\cdot)\) \(\chi_{7605}(2597,\cdot)\) \(\chi_{7605}(2747,\cdot)\) \(\chi_{7605}(2948,\cdot)\) \(\chi_{7605}(3098,\cdot)\) \(\chi_{7605}(3182,\cdot)\) \(\chi_{7605}(3332,\cdot)\) \(\chi_{7605}(3533,\cdot)\) \(\chi_{7605}(3683,\cdot)\) \(\chi_{7605}(3767,\cdot)\) \(\chi_{7605}(3917,\cdot)\) \(\chi_{7605}(4118,\cdot)\) \(\chi_{7605}(4268,\cdot)\) \(\chi_{7605}(4352,\cdot)\) \(\chi_{7605}(4502,\cdot)\) \(\chi_{7605}(4703,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((6761,1522,6931)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{1}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 7605 }(173, a) \) | \(1\) | \(1\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) |