Basic properties
Modulus: | \(7605\) | |
Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{845}(307,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7605.es
\(\chi_{7605}(307,\cdot)\) \(\chi_{7605}(343,\cdot)\) \(\chi_{7605}(892,\cdot)\) \(\chi_{7605}(928,\cdot)\) \(\chi_{7605}(1477,\cdot)\) \(\chi_{7605}(1513,\cdot)\) \(\chi_{7605}(2062,\cdot)\) \(\chi_{7605}(2647,\cdot)\) \(\chi_{7605}(2683,\cdot)\) \(\chi_{7605}(3232,\cdot)\) \(\chi_{7605}(3268,\cdot)\) \(\chi_{7605}(3853,\cdot)\) \(\chi_{7605}(4402,\cdot)\) \(\chi_{7605}(4438,\cdot)\) \(\chi_{7605}(4987,\cdot)\) \(\chi_{7605}(5023,\cdot)\) \(\chi_{7605}(5572,\cdot)\) \(\chi_{7605}(5608,\cdot)\) \(\chi_{7605}(6157,\cdot)\) \(\chi_{7605}(6193,\cdot)\) \(\chi_{7605}(6742,\cdot)\) \(\chi_{7605}(6778,\cdot)\) \(\chi_{7605}(7327,\cdot)\) \(\chi_{7605}(7363,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((6761,1522,6931)\) → \((1,i,e\left(\frac{33}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 7605 }(307, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(-i\) | \(i\) |